When the war between Lord Rama and King Ravana was over, then it was time for them to return to Ayodhya along with Goddess Sita.
But at the time of departure Hanuman was missing who played a key role in the victory of Lord Rama. Everyone searched for Hanuman. Eventually, Sita found Hanuma in a betel leaves garden . When Hanuman saw Sita , he bowed his head down to seek the blessing.
Sita was grateful to Hanuman as he had helped in rescuing her and blessed Hanuman. She plucked few betel leaves and showered on hanuman in order to bless him. Since then this tradition of offering garland of betel leaves is followed in many temples of Hanuman.
You can generally find Betel leaves being offered to Lord Hanuman in all the temples. This is due to the reason that he is very fond of Betel Leaves. Also Betel Leaves are used in every auspicious occasion be it during festivals or everyday puja. It is considered a form of Lakshmi and hence Betel Leaves is used to worship Lord Hanuman.