I had the same thing happen on my cold water supply for my washing
machine. some moron tried to seal the problem with a bunch of glue or
caulk or something...all it did was leak around it. I had to replace
that section of pipe to stop the leak.

You're leak sounds minimal... I wouldn't touch it...especially if it's
leaking slow enough that the water evaporates before it goes anywhere.

Makes me think though, that maybe the plumber screwed up other stuff
along the line and that's all you can see. Might be best to look at
anything else he did.