But there's nothing complex here. You are wrong on a very simple econ101 type level.
The covid check was economic stimulus. Like what Bush W did for example. It literally stimulates the economy every time, because for every one of you and me who don't need it and save it, by investing it in companies via mutual funds, there are people who immediately spend it on things like food, also giving money to companies.
Now here's what happens when you don't give money to companies: they have to take loans with interest. That interest is later paid by customers via increased prices, because the supply side cost is now higher.
Companies also go out of business w/o money. You now have less supply, for inelastic demand (because it's food). This increases prices.
So, econ101: prices went up. Because supply chains were affected by the pandemic, and when supply cost goes up, you pay more. If you didn't have the stimulus checks, they would have gone up more. Much more.
Paying attention in econ101 helps know this. What you missed by not paying attention, is they were referring to printing money and Not giving it to people. Like the government having to fund itself, or the king funding himself. A stimulus check is trickle up economics, and Lowers prices. So econ101 taught us the opposite of your takeaway from that class. That class was of course called microeconomics, not econ101.