It won't reduce the prices. It will merely reduce the rate of increase of those prices.
This is true, this is at least appealing to common sense. But I don't see how that excess cash was going into spending more on food and gas.
If I run a supermarket and raise prices, and people like lettuce, if they keep buying the lettuce, because $3.75 lettuce is still worth it compared to $2.00 lettuce, well, CPI can increase a lot, and demand appears to be inelastic, and interest rate increases did nothing to reverse CPI.