I know this is a recall from a while back. But I've some time on my hands. I have never come across a line in a tree. I have however left one in a tree I was working in. It was a big job and I had to finish it up the next day. However, if I found one in a tree that I wanted to climb, I would leave it alone and set my own throw line. The main reason being that I enjoy all of the process' involved in the climb.
On the other hand, lets look at it from the other side of the situation. If you want to leave your throw line in the tree FOR A BRIEF TIME ONLY, and you don't want it readily visible from ground level, here's a little trick you may find useful.
Before your decent, run your throw line over the next available TIP below your current position. Tie the ends off with a half hitch so you now have a big loop, and lower the loop bottom down so it hangs free. It should touch the ground. If not, pick a lower TIP so it does. Now, when you're about 12' off the ground just pull the end of your loop up and wedge the line in the bark. This way it's out of direct line of sight,(people by nature do not look up,) and all you have to do to retrieve it is grab a stick and snag it off the trunk. It also helps if you use a darker colored line to leave behind.
NEVER leave your rope set for future use! That's just crazy.
Later, Ron.