Abdali DID NOT GIVE back the kingdom to mughals. He appointed his own pupped to rule Delhi. Maratha's replaced him with their own puppet.
Here is the letter Abdali sent a letter to Nanasaheb Peshwa (who was moving towards Delhi, albeit at a very slow pace to join Bhau against Abdali) appealing to the Peshwa that he was not the one who attacked Bhau and was just defending himself. Abdali wrote in his letter to Peshwa on 10 February 1761.
“
There is no reason to have animosity amongst us. Your son Vishwasrao and your brother Sadashivrao died in battle, was unfortunate. Bhau started the battle, so I had to fight back unwillingly. Yet I feel sorry for his death. Please continue your guardianship of Delhi as before, to that I have no opposition. Only let Punjab until Sutlaj remain with us. Reinstate Shah Alam on Delhi's throne as you did before and let there be peace and friendship between us, this is my ardent desire. Grant me that desire."
Does this sound like a letter of a "Victor" ?
He is literally begging the Maratha's to let him keep punjab and put the maratha puppet back on the throne of Delhi.
His own "reasons" he gives for returning back sound like the "reason" chinese gave to India after retreating from Assam and Arunachal Pradesh after defeating India in 1962. The REAL REASON was that they knew they could not hold on to that territory.