Alsalam Alaikum
Here we are Motazen we are not away from you.
Regarding the subject you have mentioned before I guess that there were no mistakes, and I will tell you why.
The sentence is about a reported speech so the verb must be in the past as you said.
The right choice is (had done) because the helping verb is in the past. In another hand, regularly is an adverb referred to the main verb in the sentence which is (done) and this adverb only described the verb of the sentence without changing the tense or whatever defecting the rule.
Also, the choices are varied into
Has done
Had done
Have done
Does
Had done is the correct answer but the others are wrong because they are in the present tense
Finally, I want to remind you that these kinds of exams come from the ministry of education. So, the wrong is the least likely to be wrong because of the experience and the revision.
This is my opinion readers, if there are any other answers or even comments just share us with them
Lion Heart
sorry for being late
العرض الشجري