Recovery is possible but it depends on what caused the corruption.
If the file is just truncated, getting some partial result out is not too hard; just run
gunzip < SMS.tar.gz > SMS.tar.partial
which will give some output despite the error at the end.
If the compressed file has large missing blocks, it’s basically hopeless after the bad block.
If the compressed file is systematically corrupted in small ways (e.g. transferring the binary file in ASCII mode, which smashes carriage returns and newlines throughout the file), it is possible to recover but requires quite a bit of custom programming, it’s really only worth it if you have absolutely no other recourse (no backups) and the data is worth a lot of effort. (I have done it successfully.) I mentioned this scenario in a previous question.
The answers for .zip files differ somewhat, since zip archives have multiple separately-compressed members, so there’s more hope (though most commercial tools are rather bogus, they eliminate warnings by patching CRCs, not by recovering good data). But your question was about a .tar.gz file, which is an archive with one big member.