To go back to the otiginal question, its a matter of phonetics rather than grammar. 'p' is unvoiced, so it attracts the unvoiced 't'. Similarly the negative prefix 'in' is modified by the consonant that follows it. Illogical, irreligious, imperfect,indelible.
In Yorkshire, this tendency is still more pronounced than in other parts of the country, you will hear 'olt people' referred to, and Jim Laker, the cricket commentator, always referred to batsman David Steele as'Davit Steele'