I solved this by  not having Square do the automatic bank deposit. I turned this feature off. The money is then in my 'undeposited funds' account.  At the time of the credit card deposit to the bank, I simply choose the deposit(s )that are reflected in the deposit, then add another line to the deposit using 'square service charge ' (expense account) and a negative amount equal to the actual deposit dollar amount sent to my bank. 

That way square will show the invoice as paid (example $100 charge and $100 square payment) and the bank deposit will also match (example $100 charge, $100 less $2.00 fee recorded on bank deposit  = $98.00 deposit which matches the bank deposit)

There is no way to have this automatically happen. Either the invoice will show the fee as unpaid (in which case you can record an additional payment in the aomount of the fee for the invoice as  a 'square service charge expense 'account to clear it).  I tried this and it works and tracks but takes more time than just doing a manual deposit.  You would need to manually apply an additional payment for the fee to each invoice.  Every time.