MDM - Mobile Device Management - is a way that companies can manage the configuration of their computers, tablets and phones. Only the company that installed the MDM profile can remove it.
Intro to mobile device management profiles - Apple Support
The message that the MBA is registered to a different Apple ID is an indication that it was not prepared properly for transfer of ownership and is still associated with the Apple ID of the previous owner. You can either contact the previous owner and have them release is properly from the MDM profile and the Apple ID, or better yet, just return it and get your money back.
This is what should have been done to prepare that Mac for sale and transfer:
What to do before you sell, give away, trade in, or recycle your Mac - Apple Support