Here's what it means: Index of Jews Whose German Nationality was Annulled by Nazi Regime, 1935-1944
This is definitely our Hilda, since it shows her surname as Peiser and her maiden name as Wohlgemuth. Also, her last known residence in Germany is at an address in Berlin-Charlottenburg.
When I showed this to Walter a few months ago, he said that Hilda and her husband had already left Germany by 1935 and were living in Amsterdam (I need to confirm that he said this). That would explain why her name shows up in this annulment.
Importantly, this also provides an exact birth date and location for Hilda. If she was born in Danzig in 1906, and Elly was previously born in the nearby city Elbing, that suggests we need to look for their father Julius's origin in that area of West Prussia/Pomerania more than the East Prussian towns I had been considering before.
Also, we have said the family was from Koenigsberg before moving to Berlin when Elly was of marriageable age, but they wouldn't have arrived there until after the 1906 date of Hilda's birth in Danzig. So quite a bit to chew on there.