As I understand it, "moved with anger" at Mark 1:41 is indeed a minority reading at this verse, and one that has some manuscript support, and it certainly would be considered to conform to the "lectio difficilior" principle; the trouble is, it's simply TOO difficult a reading, almost IMHO a "nonsense" reading, being so discordant to the context as to be considered non-applicable.
How would Jesus' "being angry" result in, or be reasonably anticipated to lead into, his healing of the leper?
Who, or what, was He angry at or about?
If we presume He was angry at the disease, or if one considers that the leprosy was perhaps a Satanic manifestation that He was angry about, then why is no such anger mentioned in other examples of His' healing leprosy or other diseases, or in the casting out of demons, or even in the healing of the woman of whom He explicitly said "Satan hath bound", in Luke 13:16?
I believe the reading chosen by the the NIV is simply wrong in this case, and I DO wonder about the committee's reasons for including it, but I don't know very much about the NTTC evidence at this verse, and would be glad to learn more.