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.