"The 2020 1099-R had Code G and they did their own taxes in 2020 and this was reported as a regular rollover"

But there is no Account at this point, so there was no rollover?

"so no taxes were paid."

Unless that was a Roth 401(k) to Roth IRA, there is Conversion and there would be taxes owed.

"Rollover" is not the same as Taxable or not.

"so the client didn't open her Roth until March of 2021 when she received the check."

If she received the check, that would only be Rollover if it was deposited with the required timeframe. It is Rollover from "like type account to like type account" such as 401(k) to Trad IRA (both are pre-taxed dollars), Roth 401(k) to Roth IRA (both are post-tax dollars). Of course, an employer can offer each type of 401(k) account and the employee can have the amounts Split accordingly, as required, or still decide to do conversion on the sheltered/deferred portion (the 401(k)).

"To record the tax on the Roth conversion, do I amend the 2020 tax return"

Yes...

"to include the Roth conversion"

to Remove it. Unless there is a 1099-R for the 401(k) for 2020? And if so, was the deposit to Roth made in the timeframe of "rollover" or was that delay too long?

"or is there a way record it on the 2021 return, since that's when she actually received the payment."

Either way, it seems 2020 was wrong and needs to be amended.