If you write Final in the memo part of the check, can someone mark through it because it was not a final payment?

The memo line is simply a place on a check to provide a notation for the maker's reference. It has no legal standing if there is a dispute between the maker and the payee of the check.

In some states courts have recognized the memo line and things that indicate "paid in full" as an example but this can vary from state to state, as I have heard. We are not lawyers and can't tell you the laws of all the states. Also, from the banks perspective the check is being processed and the bank would have no saying as to such a notation or restrictive endorsement unless the check was to the bank. If the bank had any doubt as to the validity of the restriction I suspect the item would be returned with a request for a "clean" item and the payor may be subject to additional fees or costs.