Another option is just to search for the symbol itself online and see what comes up. Often Wikipedia has an entry for orthographic or transcription uses of symbols.
In this case, I think I found the answer that way:
https://en.wiktionary.org/wiki/Thread:User_talk:CodeCat/sign_%CB%A3_in_IPAThat links here:
https://en.wiktionary.org/wiki/-e#FinnishJust from the information there, it would appear that superscript /x/ represents an etymological blend of /-k/ and /-h/, which was my first interpretation. But that doesn't seem to be right. Instead, apparently superscript x represents gemination.
The article on Finnish phonology has:
Gemination or a tendency of a morpheme to cause gemination is sometimes indicated with a superscripted "x", e.g. vene /ʋeneˣ/. Examples of gemination:
https://en.wikipedia.org/wiki/Finnish_phonology#SandhiIn my opinion, that's just a bizarre (mis)use of IPA. But I guess it's traditional for some research in Finnish etymology/philology? I have no expertise in that area so I can't comment further.
In short, it isn't a sound at all but a representation of the fact that a following consonant would be geminated (doubled/lengthened) when combined with this word. It seems that this actually is a historical remnant of the original /-k/ or /-h/ ending (see above), which was lost as an independent sound but preserved in contact with another consonant with which it assimilated.
This reminds me of Italian "redoppiamento sintattico" (or syntactic gemination/doubling) where an Italian word that in Latin had a final consonant may now trigger geminiation on a following word even though the consonant itself has been lost.
https://en.wikipedia.org/wiki/Syntactic_geminationAn example given there is "Andiamo a casa" ('we.go to home'), pronounced /...ak:asa/, with a geminated /k/, reflecting the fact that Italian 'a' comes from Latin 'ad', so that now-lost /d/ has an 'echo' just triggering gemination on the first consonant of a following word.
I guess something similar happens in Finnish and that is sometimes indicated with a superscript x!
(In defense of that approach, there isn't any other obvious way to do this in IPA so some additional notation is necessary. Another option would be something like /terʋe-:/, but that is confusing and doesn't quite convey what is intended. I've seen similar notation for tones applying to a following syllable/word though.)