I think you mix up time (ie what this or that clock is showing right now), and time's speed (ie, how fast that clock is "ticking" compared to how another clock (possibly moving differently) is "ticking", as seen from a reference point.).
Like the first answer says, you should compare
dt (time's "speed"), not
t (ie, current time, the integration of that dt)
What changes when you move a clock in regard to another is that it's time's "speed" and its mass are changing, then go back to "normal".
The "current time" of the clock you are moving has changed "less" if you compare it to another clock "at rest". The clock that was moving will have, while moving faster, a slower "time speed", or "ticking rate", and then that "time speed" goes back to normal when it comes back to "rest" (compared to the reference clock). The accumulated time is therefore different, and will surely not "go back" (Going from T1 to T2
Of course this is all kind of mind boggling as the very word I used (ticking, backwards) are defined "in time", so it's kind of hard to separate whatr's physically happening from false information derived from the words themselves...