Cut off the branch and stick it in a garbage bag big enough to hold it. Stand back with a can of household bug spray (like Raid). Fumigate the inside of the bag REALLY well. Seal up the bag very well and put out with the next trash collection. Wash hands thoroughly. FINIS!
Down in these here parts most of the trees are Live Oaks scattered out all over the place and Cottonwoods along creeks and rivers. The Live Oaks worst enemy is Oak Wilt.
Folks in the cities also plant Arizona Ash because it grows huge in a hurry providing lots of shade. The AA's are notorious for Web Worms. Not sure about Tent Worms though. Maybe by another name I do but, not as TW's. I would stay away from the burning unless you are familiar with that process. You could get a can or two of Raid Wasp spray that shoots out 20'-30' or if you can get to the limb and cut that portion off without killing yourself and/or damaging the tree, then put it in a black trash bag and spray any insecticide in there making sure you saturate the little devils and seal up real tight. That is about the cheapest and simplest way of taking care of the pests.
Or, you could call TH over and let him do a little Target Practice with his .416 Rem. Mag. Just tell him you have a Giant Bull Elephant up in the tree. That should take care of things and also give you and TH a few nights free Room & Board in the local jail...LOL
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