The words remit and remittance occur relatively often in contracts. Black’s Law Dictionary gives as one definition of remit “To transmit (as money) (upon receiving the demand letter, she promptly remitted the amount due).” And here’s how it defines remittance: “1. A sum of money sent to another as payment for goods or services. 2. An instrument (such as a check) used for sending money. 3. The action or process of sending money to another person or place.”
For purposes of conveying these meanings, remit and remittance have a nineteenth-century air about them. I’d have no qualms about replacing them with the less-fusty alternatives pay and payment, or transfer (the verb and the noun), as in the following examples:
Upon Substantial Completion of each System, Owner shall remit to [read pay] Contractor half the amount retained with respect to that System.
… an amount as that Lender or the Administrative Agent, as applicable, determines to be the proportion of the refunded amount as will leave it, after that remittance [read payment], in no better or worse position than it would have been if …
Some contexts might require a more specific alternative, such as refund (verb or noun).
And seeing as remittance is an abstract noun, you may be able to replace it with a verb (see MSCD 16.7.):
If at any time legal restrictions prevent the prompt remittance of part or all [read If Acme is unable to pay promptly any] royalties with respect to any country in the Territory where the Product is sold, …