Are received BTCs really mine?
Wallets will only consider outputs to be theirs if it is something that it can spend from. This usually entails checking the output script against the set of scripts that your addresses will be used to generate. So even if you can sign for something, if the script does not match any of the scripts stored in your wallet, then it will not consider that output to be yours.

If the output was a P2SH output, then you would need to have the redeemScript in order to spend from it, so unless the sender shared that with you (and if they did, you could check for any nastiness), your wallet won't even know that you could spend that P2SH output.

Also, there is no "claiming the balance" or claiming of any sort except when you spend an output.