If you have a boiler or if it’s laying in your yard and you need to get rid of it, burn it. Otherwise if it’s not in your yard leave it lay. It’s basically at the rock bottom of BTU charts and it doesn’t smell pleasant when burned either.
There’s a unique forest about a mile behind my cabin that has nearly every species of tree back there versus our normal forest that’s primarily aspen and evergreen. Saw a big uprooted clump of trees with one big truck in the middle....score! Turned out it was basswood so after one cut I walked away.
Basswood . . . carving . . . I believe basswood was traditionally used for carving duck decoys. (Maybe also cedar, which is more rot resistant.) It's somewhat of a weak, light wood, but it has its uses. Holds paint well, I'm told.
Between deer camp and our home property, we have a total of seven wood burning appliances and I like burning Basswood in two of them: the sauna stove at deer camp, and the stove we use to boil maple sap here at home. Provides a quick, hot fire, good for heating up the sauna in short order; for the sap stove, Basswood and Aspen are my favorites...….splitting it wrist size and with a small blower it produces a roaring boil for the sap pan on top of the stove. Whenever we see a Basswood blowdown around camp, we grab it. Earlier this summer, a friend of a friend had a large tree in their backyard snap off about ten feet up, they know I burn wood in an OWB and asked if I wanted it; I showed up with all the cutting equipment and the homeowner said "I think it's a Basswood so you probably don't want it" and I replied that I'd gladly cut it up and take it. He looked puzzled so I explained that I like to use it to make maple syrup; next time I drove by that place I stopped in and thanked him again for the tree, handed him a bottle of syrup and said this is what happens when I burn Basswood