"I also need to explain this to the client (and others if they receive similar letters)."

I don't see where you told us MFS, MFJ, HOH, Widow(er), or ? Because in general, most of what you told us is moot. Nothing about 2018 or 2019 AGI applies for the EIP submission as Reconciliation on the 2020 return.

It's very simple: Use the 2020 info to see if they qualify or not, for how much, and then compare that to what they got. Remember to add $10k (which is for one child) to the phaseout limit which is based on the filing status. Then, adjust down by 5% from the limit start to AGI.

https://www.irs.gov/newsroom/calculating-the-economic-impact-payment