This reminds me of something I was told by a Bianchi USA sales rep back around 1990, when I worked in a Bianchi dealership. The rep was there to examine a frame with a crack at the junction of a seat stay with the seat tube lug, obviously a consequence of having been overheated in the brazing process. The rep said, "No problem. We'll send out the replacement frame immediately." I asked what they were going to do with the cracked frame, whether they were going to show it to someone from Bianchi of Italy for reimbursement.

He laughed and said that Bianchi of Italy sold their bikes to Bianchi USA without warranty and that they thought the idea of offering frame warranties was hilarious, especially for lightweight, high-end frames. He once heard an upper-management Bianchi of Italy guy teasing a Bianchi USA guy by saying that, sure, we can start selling racing bike frames with a warranty. Of course, they'll weigh a kilogram or two more than they do now.

Sorry---there's almost certainly no bike company anywhere in the world that would cover frame damage caused by impact from a tree branch or the equivalent under warranty. Offering a frame for half-price or for some such discounted price is the industry-wide approach for accommodating situations like yours. If it were me, I'd let it go and follow the suggestion by other people in this thread to just wrap the tube in carbon and install a bash guard.