In the Web2 world, when you do an operation you are unlikelly to care about of even be aware of its processing cost. I believe it should be the same for meta-transaction. The end user who signs it doesn’t care.
The relayer does care about the relaying cost! Depending on the situation it’s either going to accept it as a lost, ask for repayment in fiat offchain, or ask for a repayment onchain. In that last case there should be a protocole, including signatures, that ensures relayer and repayer are on the same page. But again, unless the user actually the repayer, it should not care about gas. Only the repayer does. Thus, the repaying protocole shouldn’t be part of the meta-transaction signature/verification/replay-protection/ordering.