Without lifting the rear end, I was able to see discoloration around the boot. I'm going to take the car back to the shop that replaced the half-shaft. When I talked to them on the phone, he said that they may have put more grease (or whatever is in there) than needed and it oozed out when it heated up. They're going to get it up in the air and inspect. I'll update this thread when I get the car back.
While it's in the shop, I'm going to get my tie rods replaced and lower suspension brace installed, so I have that to look forward to...