Nest in a tree

So I want to cut down a tree on my urburbian lot (for various reasons), then use the wood for hugel. Upon closer inspection, there is indeed a nest in the tree. On most forums, I would feel like a total moron for asking this, but I know permies are different.. so.....

What do I do about the nest? I'm not even sure if it's used anymore (can't climb that high and I've never seen a bird in or near it). Moving it doesn't seem very viable or useful. Just cutting down the tree and discarding it seems, well, callous.

Am I just overthinking it?

The nest is almost certainly vacant this time of year.

Your location mentions Salish, which is a West Coast of North America native language and ethnic group. The location option is there so that people are better able to help one another. Few will get this reference. If you are in coastal British Columbia or Washington, stating that information clearly is likely to be useful.

Voila!