Texas demand letter only partially met

[Mike Mitchell]

I've sent a demand letter on a note in TX and only a portion of the total has been paid. I'm holding the money order as it seems that I have read that a portion cannot be accepted or it interrupts the process. If so, am I required to refund any portion paid after the demand letter is sent? It doesn't look as if they can come up with the remainder and I'm not willing to work with them anymore as there have been many late payments and a couple of demand letters have been sent and met in the past.