New house has small tree stump close to house. What can we do to remove it, and not attract termites?

Depending on how much time you have you could also get some tree stump dissolver from your local nursery. The powder is mixed with water and poured down holes you drill in the stump. After a few months the cellulose in the stump kind of dissolves and the stump falls apart in chunks. I've done this to 3 stumps over the years. If the wood is a hardwood it may take a year. Cheap, effective, slow. If you're afraid of termites you could spray with an insecticide every few weeks, that should keep them away till the stump dissolves.