This gives me anxiety, too, so I get it. If someone is coming to do work in the house (like fix furnace, etc.), I always ask H to work from home that day. When I lived by myself, I tended to leave if I thought they'd be coming.

Though once, when living alone in an apartment, they really freaked me out. I assume they'd come in to check on potential gas leak while I was out, but didn't leave note or anything. I walked in to find stuff that had been on my stove (a pan, etc.) sitting on my dining room table. So I worried there was someone in the apartment and nearly called 911 (think I called my mom instead, for whatever reason).

It was really wrong of them to steal things...I'd report it.