From an earlier answer

This is a somewhat contentious issue and one that is clouded by numerous parties postwar who argued that the Greek theater was a vital delay for Barbarossa. Obviously, the notion of Greek resistance and a nationalist narrative fed into the delay hypothesis, but it also received support from British quarters who argued that the deployment of W Force was not a waste of lives, but a vital delaying action. Postwar German generals also popularized this narrative. Keitel would claim postwar the Greek adventure was a "great delay," without which "events on the Eastern Front and the war as a whole would have turned out very differently."

The strongest support for each of these narratives is that Barbarossa was initially set to commence in mid-May but later got pushed back to June. Planning for Operation Marita ran concurrently with planning for Barbarossa and the growing concerns with occupying the whole of the Balkans led to a deployment of troops needed later for Army Group South's invasion of the southern USSR. However, there is not a straight line between Greece and the June date as there were other factors behind the delay. The spring rains created concerns within both OKW and OKH about the viability of a May invasion. Guderian would later claim postwar that he had personally reconnoitered the Bug River and found them passable and the actual meteorological data for 1941 shows that rainfall was not above average in the various marshaling points for the German invasion. Nevertheless, this was a viable concern for German planners as an unexpected storm could bog down an invasion before it started. The need to train and reequip formations was another pressing factor for German planning. Even though the Germans went about planning for the invasion with an almost cavalier attitude to Soviet capabilities, they could not escape the material constraints of equipping an army for such a vast undertaking. For any planner in OKW and OKH that wanted a delay to better prepare for Barbarossa, Marita was a godsend as it provided an overwhelming justification for pushing back Barbarossa until a time that it was more manageable for German forces.

The issue of the delay possibly caused by Marita has overshadowed the actual benefits that Germany accrued from invading Greece. Firstly, it secured Germany's southern flank and prevented the British from operating against Romanian oilfields while German forces were preoccupied with the USSR. The swift invasion of Yugoslavia also helped cow Germany's Eastern European allies like Hungary who were not that enthusiastic about participating in the grand crusade against communism. Secondly. Marita helped Barbarossa achieve a degree of strategic surprise. A number of Soviet intelligence forces initially warned that the deployment of German troops to the Balkans was the start of a larger invasion of the USSR. Although Soviet troops went on alert, they found there was no invasion forthcoming. This "boy who cried wolf" mentality did play a role in the dismissal of later German preparations for Barbarossa. The deployment of German troops to the Balkans created much confusion as to what Germany's true strategic aim was, especially in light of overtures to Turkey, German involvement in the Iraq coup, and the creation of DAK, all of which might have suggested a broader German strategic reorientation to destroy the British in the Mediterranean.

But Marita did degrade German military capabilities in several significant ways. Aside from occupation costs, the troops involved in Greece arrived late to the Soviet campaign and their equipment was worn-down. Army Group South lost six infantry divisions in the opening stages of Barbarossa because of Marita. This left a number of the initial attacks understrength and more reliant upon Romanian and Hungarian contingents than their neighbors. Both of these satellite armies emerged out of Barbarossa in quite rough shape because they had to conduct operations that were outside their capabilities. This combat degradation continued over the long-term and would come back to haunt the Germans when they were dependent upon the minor Axis powers to guard the Stalingrad salient in the campaign the next year.

The invasion of Crete also cost the Germans dearly in terms of transport aircraft and soured German planners on the use of airborne troops. There were some tentative plans to close off the encirclement of Soviet troops with airborne forces, but the losses incurred in Merkur precluded this. Perhaps more importantly, the loss in transport aircraft further hobbled a German airborne logistical force that already was inadequate for the task at hand. The Germans had pioneered a number of elements of resupply by air in Fall Gelb, but this was less viable in light of German losses to take the island. The Luftwaffe was able to cobble together enough forces in Barbarossa to resupply over-extended lines, most notable at Demyansk and Kholm, but could only do this by stripping training units back in the Reich. This short-term expedient was problematic for the Luftwaffe's transport forces which by 1942 was operating at a negative ration with losses in aircraft outstripping their resupply by a ratio of approximately 2:1.

Ironically, one of the most central planks of the delay hypothesis itself rests on a set of highly dubious propositions. The basic idea is that the month's delay meant that German forces might have reached Moscow one month earlier and captured it before the onset of winter. British General Henry Wilson, the commander of W Force, would tell a group of repatriated British and Commonwealth POWs in 1943 that "Greece was responsible for the six weeks’ delay which allowed the winter to intervene." Although "General Winter" remains a popular trope even in 2015, it is one historians of the Second World War have long since discarded as a significant factor in Germany's failure to defeat the Soviets in 1941. German forces were simply too small and inadequate to complete the job and the Soviets were able make good their tremendous losses through a herculean effort that few expected in 1941. Nor was the occupation of Moscow the plum strategic target that some postwar commentators claim; although the loss of the capital would have been a blow to prestige and some hindrance to the Soviet war effort, it was not central to the Soviet war economy. The Stalinist industrialization drive of the 1930s allowed for excess productive capacity and it could have adjusted to the loss of Moscow just as it did with the loss of other Soviet cities.

So while Ochi Day and the valor of Greek resistance is something for Greeks to be rightly proud of, the impact of Marita on the larger German war effort was pretty peripheral. It added an extra burden on an already overtaxed German military establishment and gave a pretext for a delay that German planners were already floating.

Sources

Citino, Robert Michael. Death of the Wehrmacht: The German Campaigns of 1942. Lawrence: University Press of Kansas, 2007.

Militärgeschichtliches Forschungsamt, Germany and the Second World War, Volume III: The Mediterranean, South-east Europe, and North Africa, 1939- 1941 Oxford: Clarendon Press, 1995.

_. Germany and the Second World War. Volume IV, The attack on the Soviet Union. Oxford: Clarendon Press, 1998.