In order to fill in the blank with the most suitable form of infinitive, we need to understand the meaning and usage of 'rather than'. 'Rather than' means the same as 'would rather', which means 'instead of' or preferring someone or something over the other. If 'rather than' is used in a passive (voice) sentence, we use the word 'to' along with the verb. In an active sentence, we do not use 'to' with the verb. The verbs without the marker 'to', are called bare infinitives.
As the given sentence is in active voice, we will use the bare infinitive here.
Option A - 'Finished' is the past form of the verb 'finish'. As we need a bare infinitive (original form of the verb), we can't use 'finished' here. Hence, option A is incorrect.
Option B - 'To finish' can't be used here as the verb is in its original form with the marker 'to'. As the sentence is in active voice, we can't use the infinitive with 'to' here. Hence, option B is incorrect.
Option C - 'Having finished' can't be used here, as 'having finished' is not a bare infinitive. Hence, option C is incorrect.
Option D - 'Finish' is a verb in its original form and is a bare infinitive. Hence, option D is the correct answer.
'Despite of their parents' scoldings, they watch TV rather than finish their homework.'