How to move a deposit made into the check register against a customer's invoice in accounts receivable instead?

Yes. Record the payments as they happened as AR Payment transactions. As you do, apply them to the appropriate invoices.

Then, edit each problem deposit, delete the incorrect line items from it (Edit | Delete Line), then use the Payments button at the top of the deposit form to add the appropriate Payment(s) you just created to it.

Once the deposit total is the same, then save it.

I think there is some confusion with my question.

I am new at my company and didn't realize that some of the deposits listed on bank statements were actually payments received via credit card to be applied against open invoices in our AR, so I mistakenly went into the check register and entered the credits from bank statement that way.  I am trying to get things caught up in Quickbooks from 2021 and had been told the credits on the bank statement were refunds of freight charges....  this was incorrect and now I've reconciled a years worth of bank statements with these applied incorrectly.  I need them to go against the open invoices in AR.  Is there a way to go back and fix these without messing up my reconciliations in QB desktop?

Please be as detailed as possible.

Thank you so much for any help!

RE: I think there is some confusion with my question.

If there is, I can't tell where. Your description seems clear.

RE: ...were actually payments received via credit card to be applied against open invoices in our AR, so I mistakenly went into the check register and entered the credits from bank statement that way.

If by 'credits' you mean deposits of money received from customers, then my previous answer is what you need to do.

RE: had been told the credits on the bank statement were refunds of freight charges.... this was incorrect and now I've reconciled a years worth of bank statements with these applied incorrectly.  I need them to go against the open invoices in AR. 

I don't think it matters what your customers you paying you for. Payments against A/R are all the same. In this case, again my previous answer is what you need to do.

RE: Is there a way to go back and fix these without messing up my reconciliations in QB desktop?

Yes, see my previous answer.