With pronouns, inte can go in either place in a sentence like this. With a noun, inte would always go after the verb. Det överraskar inte mamma 'That does not surprise mom' – you can't have inte last in that version.
More about this under 1.2 in this post: https://www.duolingo.com/comment/8970470
As Arnauti has already explained, "inte" can be of either side of "mig" in this particular situation, though they give slightly different impressions. Putting it after "mig" like in this sentence is just a straightforward "That doesn't surprise me", whereas the sentence "Det överraskar inte mig" puts more emphasis on the "me", implying that it does not surprise me specifically, though it may surprise someone else.