Here's a breakdown of the US COVID spend. I don't see how this is an inflation driver. The only one that might be is the direct payments, but that's less than a quarter of the total, and for everyone who didn't need that, there's probably someone else who did to pay rent/mortgage etc., i.e. every day bills and not just blowing it.
See how much COVID relief has been spent and where the money has gone with the #COVIDMoneyTracker tool.
www.covidmoneytracker.org
Inflation is being driven by the supply chain problems with Covid, as best I can tell. Americans have a higher saving rate now than in decades, so its not demand - its limited supply driving up prices which drive up the indices used to calculate inflation. I expect this will settle down. If the Fed is estimating inflation at 3.4% for the rest of the year but not upping interest rates, I expect they are not that concerned, and they know more than me on this subject.
BTW, inflation (low digits) is not necessarily a bad thing.