The party's Assistant Office Secretaries Abdul Latif Jony and Asadul Karim Shahin on Saturday took the card to Awami League President Hasina's Dhanmondi political office.
The two arch- rivals, who alternately ruled Bangladesh for the last two decades, have not come face-to-face for a long time.
But they exchange greetings ahead of the Eid and the Bengali New Year every year.
Khaleda is currently on her way back to Bangladesh from Saudi Arabia where she performed Umrah.
An Emirates flight carrying the BNP chief, her elder son Tarique Rahman and other family members left Jeddah early on Saturday.
Her Press Secretary Maruf Kamal Khan said Tarique, his wife and daughter will start for London after a break in Dubai while Khaleda will be on her way to Dhaka.
The former prime minister and her family members had gone to Saudi Arabia on July 20 to perform Umrah, a pilgrimage to Mecca that can be undertaken any time of the year, at the invitation of Saudi King Abdullah Bin Abdul Aziz.