Specifically on that image, the rear turret hasn't been removed. That is a very standard sun shade common to many navies: warships of this era rarely had air conditioning, the ships are made of steel (with the upper deck sometimes covered in wood or a similar material), and can turn into ovens easily. The sun shades help keep that down. This overhead from the Panama Canal shows part of the turret under the shade, this January 1940 photo shows the turret is still in place, and this US Navy photo shows them on several dozen ships.

Moving onto your main question, what modifications did they receive, the first thing to note is the ships were very old pre-dreadnoughts. They were slow, their equipment was out of date, and in a modern fleet battle they would be extremely vulnerable. Even at Jutland the pre-dreadnoughts did little: Campbell's analysis of their ammunition expenditure in Jutland: An Analysis of the Fighting shows the only time they fired their main guns was after the main battle was over at non-existent submarines. The Germans did not expect these ships to face off in a major fleet battle, nor could any reasonable rebuild make them capable in a modern battle. That affected the level of modifications: the modifications a ship to deal with a certain threat level and logistics system, so a lower threat level will mean less extensive modifications compared to ships expected to see major combat.

Modifications in general are something that can be unclear. They may not always be mentioned in some secondary sources, and even when they are different sources can disagree, usually over minor details like the number of AA barrels. For example, for general information on a wide variety of ships I prefer Navypedia, especially for ships where I don't have a detailed source. But this is not always correct and does not cover all the areas that can be modified. Thus whenever possible I recommend cross-referencing any modification claim with photographs, reputable drawings, and published authors (who often have photographs and drawings in their works), and fortunately in this case we have good information for before the war. During, however, that drops away.

In the 1920s the main modifications were to the boilers, upgrading eight from coal to oil. Photos also show the funnels were revised, with the forward funnel now trunking into what had been the second. While I have no information on the specifics for this case, in other navies (like Japan, the Nagato class went through several funnel revisions) this was mainly to reduce smoke from interfering with fire control, and I also note that the foremast grew taller, more substantial, and has an enlarged fire control position. The other major modification was adding anti-aircraft guns. The Panama Canal photos confirm she received four 88mm Flak mounts on the aft deck, the standard German heavy AA gun in the 1920s and used on smaller (and less important) ships through WWII. There also appear to be four pedestal mounts for light AA, though the guns themselves are absent. The ships reportedly received four single 37mm guns, but few single mounts were built and largely sent to smaller ships and U-boats. Thus these are probably for the four 20mm guns also mounted, which could be removed from the pedestal for maintenance.

I cannot quickly find photos of the ships after 1940. However, it is probable that they received some AA upgrades late in the war as Navypedia states, though if the ships received Bofors it would be very late in the war as other ships were higher priority.

Not a complete answer to your question, however, but worth noting that the rear turret is not removed in that picture. What you are looking at, rather, is a canopy constructed over the decking (including covering the rear turret). Warships of the period (this was common from the ironclad era through the early Dreadnought battleships) had reasonably poor ventilation, and particularly when coal-fired could become quite hellish below decks even in temperate climates. The problem became more acute the hotter the outside weather was. Ergo, when travelling through the tropics, a temporary canopy would often be strung over the deck to both reduce direct sunlight heating of the ship, as well as give the crew somewhere they could go when off-duty where they could recover from the heat. You'll also see this on ships hosting or transporting dignitaries, diplomats, rulers, etc.

These could, at times, practically cover the entire ship - consider some of these photos of the turreted monitor USS Onondaga.