Tweeter Dome Puncture

It is probably the dust cap you are referring too. Should not affect the speaker.

Yeah, the dome is the driven element of the tweeter - it's what moves the air. Although a pinhole sized puncture in and of itself is probably not going to appreciably change the sound of the tweeter, it may be indicative of some sort of past impact that could have damaged it in other ways you can't see. Depending on who made the driver and how old it is, you may be able to either buy an identical replacement whole driver, or sometimes you can obtain a kit to replace just the dome/voicecoil/leadouts assembly while still reusing the same motor/faceplate structure for less money. In either case it probably won't be terribly expensive if it is available, but research it first to make sure it can be easily done, and maybe have the seller take that expense into account on the price.

Hello,
It is possible that the dustcap was dented in the past, and the method used to "pull" the dent out was to take a pin or needdle and insert it into the center of the dent, angle it down, and gently pull upwards to pop the dent out.
The pinhole you see could be the result of that? Just a thought! As stated above, sound quality should not be affected enough to be audible.
Thanks!