Well, in the South, they may write "get," but they pronounce it "git," and writers sometimes even spell it that way to represent the dialect. I would be surprised if it were not in Mark Twain that way, for instance.
I found that the infinitive of "to go" is "gitmek" but the corresponding present stem is "gider-". It this sort of consonant mutation? Do all verbs with infinitive stems ending in -t follow this pattern?
Consonant mutation happens not just to verb stems, but whenever the following consonants are trapped between two vowels: k, t, ç, p. (I think of ketçap/ketchup). Explanation, examples, and exceptions at TurkishBasics.com. It is also discussed in the Accusative Tips & Notes