The border was contested several times in the 1930's and 1940's by Nazis, especially by the nazified German minority living in Denmark. However, their attempts on making the border an issue ended up being suppressed by Auswartiges Amt (AA) who was the dominant power player in the Danish-German relations. And the AA had the backing of Adolf Hitler in this, so even the SS had to lay low when it came border revision activism.

So why did Hitler not see the Danish-German border as a problem?
As Gerhard L. Weinberg writes in his "Hitler's Foreign Policy, 1933-1939", Hitler simply wasn't a "border revision politician" and had repeatedly attacked such politics and politicians in the past.
It wasn't because Hitler had any respect for existing borders, on the contrary, but because his racially motivated Lebensraum project to the east, which far exceeded in scope any Versailles Treaty border revision, was what was truly important to Hitler.

Before the outbreak of war, Hitler wasn't to keen either on increasing Germany (The Reich proper) if it meant non-German minorities living inside the border, something that he saw as problem with regards to both Denmark and South Tyrol, another area that Hitler didn't annex despite a large German speaking minority and it having been annexed by Italy after the first world war.

Other factors may have contributed to as why Hitler and other prominent Nazis didn’t see the 1920 border as a problem; Denmark had been totally neutral during the first world war. The Danish minority in Germany before the 1920 plebiscite had followed at rather disciplined “Do your duty, demand your rights” strategy, and had been loyal to the German state, also when fighting in the German army. The German minority created by the 1920 border revision had also been treated well by the Danish state, and they were allowed them to have German language schools and kindergartens, and otherwise have the same cultural privileges and freedoms as native Danes did, like publishing German language newspapers etc. All in all, the Nazi activist elements among the German minority had so few cases of oppression to rally around, that they suspected the Danish state of “repressive tolerance”.

After the occupation of Denmark and as the war progressed, it became ever more difficult to make a border revision, simply because it would jeopardize the ever more important food supplies coming from Denmark; 1/3 of all butter consumed by the Wehrmacht 1943-45 was Danish, so was 14% of all its meat consumption. (see https://doi.org/10.1080/03468755.2013.817778)
The author of the article makes a convincing argumentation, that keeping this food supply flowing was seen as so vital for Germany, that it can be seen as the main reason why the German occupation of Denmark in so many aspects, was a “special case” compared to the rest of Europe.