Explanation:

The original sentence is erroneous.

Reason: The correct idiomatic expression in this sentence is 'drag their feet' and not 'drag with their foot'.

Drag one’s feet (Idiom):

Meaning: Be deliberately slow or reluctant to act.

E.g.: We can't be late for the dentist, so quit dragging your feet and get in the car!

 Hence ‘drag their feet’ should be used in place of ‘drag with their foot’ to make the sentence grammatically correct.

Among the given choices, only option C replaces the given bold part most appropriately.

The sentence after replacement becomes:

In romantic relationships, couples usually drag their feet when it comes to initiating talks regarding marriage.

Option C is hence the correct answer.