Oh no, it's another impossible mark! Silver cross

I'm not sure a loupe will be any better: those were done with macro telephoto on a Lumix! I'll have a go though.

Fid, Austrian would make sense, it has that look to it.

 

And yes, I need to find a nice pale garnet. That other cross is interesting: smaller, but the same design.

 

on a second glimpse that TT could be an F - either for fremd or for Lwow.

 

That's a thought. I'll have another peer at it.

 

It doesn't look life an F to me. If for Lwow, the F would be incorporated in another, general Austro-Hungarian mark.
Austro-Hungarian import marks look like these:

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Marcasites in Austro-Hungarian jewellery are generally of a more silvery colour. Gemstones are rarely set with delicate prongs, like the smaller garnets on your cross, but with very thick prongs, a closed bezel like the navettes, or the much preferred pinched bezel like on this garnet cross from my Austro-Hungarian collection:


The central pearl is set with those typical Austro-Hungarian thick prongs. Austrians still use those a lot.
This cross pendant is in the classic Austro-Hungarian style btw, 19th century Renaissance Revival, which is still popular in a slightly modified way in parts of Central Europe. This is of the late Austro-Hungarian period, made in Slovakia with Bohemian garnets.