I assure you that this fungus has nothing whatsoever to do with the tent caterpillars. Or even the sapsuckers that have obviously been busy!

What it DOES have to do with is the site of the broken branch or badly pruned limb. The fungus is the fruiting body of an organism feeding on live or dead wood deep within the tree body. I honestly don't know if this is simply decomposing the dead interior wood, or is a disease causing fungus. The fungus was introduced into the tree's system when that branch broke off, or was carelessly pruned.

I can tell you that there is nothing you can do to 'fix' or 'cure' the tree. However, depending upon the species, trees can live more many years with this kind of activity going on. Keep your tree well-mulched, if you don't already.

Don't try to remove the fruiting body as you may cause further injury to the tree. There is no spray that will get rid of it, either. The mass will eventually disappear, but the fungal organism remains deep inside the tree forever. It is likely to 'fruit' again around the same time every year.