All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
There is no objection to gifting a non-Muslim.
'Umar ibn Al-Khattaab gifted his polytheist brother in Makkah a silk garment that was given to him ('Umar) by the Prophet .
The scholars concluded from this that it is permissible to keep ties with a non-Muslim by gifting him or giving him charity.
Tarh At-Tathreeb reads:
"This (narration) is proves the permissibility of keeping ties with non-Muslim relatives and being kind to them, and that it is permissible to gift a non-Muslim even if he is belligerent."
Allah knows best.