d- does not mutate to th-.
The various mutations following possessives are explained in the 'hints and tips' for this section.
Here, ei means 'her' and ei (her) is followed by an aspirate mutation or by adding h- in front of a vowel. Where ei means 'his', it is followed by a soft mutation.
'To pay, paying' is talu - an aspirate mutation changes it to thalu.
Thanks - I think I had seen this sentence just after seeing talu mutated to dalu, which is why I was thinking it was the d that had mutated. I have since seen another thread on this subject, so understand it more now!
If you make a point if always reading the hints and tips it should make things easier! We do try to keep them updated to address the questions we see being asked.