Bummer your new GTP has mites. Here is a good thread about how to treat GTPs with Prevent-a-mite. Since they are arboreal there are a few tips like spraying the perch.
http://moreliaviridis.yuku.com/topic.../Proven-A-Mite
How big is it right now? Maybe post some pictures. With green trees you don't want to handle them for the first year or so due to how fragile their spines are. After that they can be very nice snakes to handle but with most things you may have to work with them a bit to get them to trust you. Ours are all very mellow.
Oh, and Signal has a great article about handling tips to avoid bites. Also, do you know what locality it is?
http://www.signalherp.com/whybebitten.pdf