Angry neighbor because leaves from a lovely Madrona tree fall on her walkway. I don't want to cut the tree. Should I offer to sweep her walkway so the leaves don't bother her?

This couple has cut down almost all the trees all around their house. The only ones left are my wooded property. They asked if they could cut (one huge branch) of this beautiful Madrona, and I really feel that it would kill the tree. Now she is furious, calling me a terrible person because I won’t cut it. I thought I could offer to sweep the walkway myself, or hire someone to do it every week in the fall. Suggestions? It’s such a shame to have this happen between neighbors, and I really do want to cooperate—I just don’t want to cut this tree.