The frame is not the matte, it's a mat--they are different words for different concepts. There is no ambiguity or uncertainty. But I would also suggest 'frame' as it's much less likely to cause confusion.
As for the opposite of glossy, there are various spellings that seem to create discussion. Is it matte, or matt or mat?
The way of resolving this is to refer to the best COMPLETE dictionary for your region. So don;t use a compact or shorter revision, but go to Merriam-Webster complete, or the big OED or whatever your reference is. You are likely to find that Oxford suggests MATT, and M-W suggests MATTE. Both will refer to the other variants of spelling, but the one that is listed first is the dictionary's preferred version.
This is one of the rare cases where the longer (some would suggest more pretentious) variation is the US one :-).