I truly don't believe it has anything to do with Gleevec. I have been on Gleevec since 2005!
Way back in the early 1990's I went to a doctor with the same thing you are talking about, and the doctor mentioned the Raynaulds, however you spell it. I had quit smoking way back in March of 1989. Which is a good thing as it constricts the blood vessels.
However a few years ago I went to a seminar by an arthritis doctor. I asked him the same question about the hands and fingers. Especially some of the fingers turning white when they get chilled, mainly in the winter, or while holding something cold. Then to warm them, putting them in warm water and they turn sort of a purple. It was strange, as he didn't know I had CML, he said that was a sign of an immune disease.
The doctor at MdAnderson told me that CML had been working on me long before diagnosed. I think we are predisposition to certain things with certain environmental factors.
I read an article sometimes ago that sometimes the blood in the fingers actually gel, and you need to thaw them in lukewarm water not hot. It is not that the blood is constricted. Therefore, if that theory were true, I would rule out Raynaulds. Actually I don't know the true cause. I do know I had this problem long... before.... Gleevec!!! Even if you were to go to a drug, you would just be trading one daemon for another demon, they are all toxic!
I bet you will find a lot of people on this board who had immune disorders long before TKI's. I would blame it on the CML before I would blame it on the drugs. Not that drugs don't have their own nightmarish side effects.
Right now I am dealing with tendentious in the left arm and hand. I go to a chiropractor and do physical therapy. I alternate between cold packs and hot wax treatments.
I Don't think it is the Gleevec.