The relevant law is
18 U.S.C. 922 (k) which reads:
"(k) It shall be unlawful for any person knowingly to transport,
ship, or receive, in interstate or foreign commerce, any firearm
which has had the importer's or manufacturer's serial number
removed, obliterated, or altered or to possess or receive any
firearm which has had the importer's or manufacturer's serial
number removed, obliterated, or altered and has, at any time, been
shipped or transported in interstate or foreign commerce."
Based on a "I don't want to go to jail" reading of that statute, the Sig Mosquito has a serial number that has been altered. Anybody who knows that the serial number has been altered is guilty of a federal felony crime if they transport, ship, receive, or possess the Sig Mosquito.
I don't see anything in there about "it is OK if it is only on the frame" or "it is OK if there is a serial number somewhere else on the pistol"; but I don't know everything there is to know about this law and it is possible there are other statutes or case law out there. If anyone wants to share those, I would be interested in seeing them.
Looking at Sig Mosquito prices online, the pistol is worth less brand new than what two hours of a lawyer's time go for. I'd just get rid of the pistol at this point (or at least the part with the altered serial number). It isn't worth the potential legal costs to keep it.
You could also try resolving it with the ATF yourself; but you lose the advantage of lawyer-client confidentiality if the ATF decides they want to prosecute someone. If you do go this route, make sure you get the answer in writing directed to the owner of the pistol.
ETA: Found this decision
U. S. Vs. Carter, 421 F.3d 909 from the 9th Circuit discussing what "altered" means under 18 USC 922(k). The holding here was:
"In sum, the ordinary meaning of the phrase "altered or obliterated" cannot support the contention that a firearm's serial number must be rendered scientifically untraceable for Guideline § 2K2.1(b)(4) to apply. To the contrary, nothing in the language, structural context, legislative history, or purpose of § 2K2.1(b)(4) suggests that any defacement must make tracing impossible or extraordinarily difficult.
We hold, therefore, that for the purposes of Guideline § 2K2.1(b)(4), a firearm's serial number is "altered or obliterated" when it is materially changed in a way that makes accurate information less accessible. We further hold that, under that standard, a serial number which is not discernable to the unaided eye, but which remains detectable via microscopy, is altered or obliterated."
This would only be relevant to the 9th Circuit though. Texas is in the 5th Circuit which might take a different view. Suffice it to say though, anyone caught in possession of that Sig Mosquito by law enforcement is going to get to go to court and hash that issue out. I haven't priced out what it costs to take a federal felony to the appellate level; but I bet you can buy a lot of new Sig Mosquitos for that price