/t/ → /k/
Now the plosive alveolar /t/ is followed by a sound that is produced at the back of the mouth, a velar (a /k/or a /g/), so the /t/ is assimilated into a voiceless velar /k/. As you can see, the place of articulation changes, but the manner and the voicing (voiceless) are kept.
/t/ (followed by /k/ or /g/) becomes /k/
And here are some natural ocurring examples: