No-one really seems to know
where exactly Serviettenknödeln originated.
The German Wikipedia entry says that before the 1930s
they were only known in the regions of Hamburg,
Thuringia and Upper Franconia (all in Germany):
There is a Viennese cookbook by Louise Seleskowitz (1905) that mentions Palffy- Knödeln (very similar to Serviettenknödeln, except they use brioche rather than bread rolls and add speck):
"Palffy" is a widespread Hungarian name also frequent in Slovakia, and with the proverbially ubiquitous Czech and Slovakian cooks in Austrian upper middle class households during the Empire, it's certainly possible that the original recipe came from that area of Central Europe.
However, the Czech Wikipedia article is only talking about the "bread roll knödel" (houskový knedlík) and does not discuss the roll of the napkin in the production at all:
So we mighty have to leave the decision to the same jury that is still out on whether lamingtons are Aussie or Kiwi by origin.
And as far as your knödel-related garlicphobia is concerned: of course, Semmelknödeln (of which Serviettenknödeln are a subspecies) aren't usually produced using garlic. However, they are a very popular side to Schweinsbraten, because they are so ideal to soak up the gravy. And that gravy, if it's any good, is made with quite a bit of garlic. So Semmelknödeln and garlic are actually a match made in Central European cuisine heaven.