The sunnah of feeding (poor) people
This is covered in both sahih's and the three sunan books
A person asked Allah's Messenger (ﷺ) . "What (sort of) deeds in or (what qualities of) Islam are good?" He replied, "To feed (the poor) and greet those whom you know and those whom you don't know."
(See in Sahih al-Bukhari 1, 2 and 3, Sahih Muslim, sunan ibn Majah, sunan abi Dawood and sunan an-Nasa-i)
Note that the hadith doesn't explicitly say that feeding -only- poor people is the best quality.
From this hadith we can conclude that feeding people at this occasion is permissible and could be a good deed.
The would-be bida'h of giving food at a Khatmah
Note that there's no source saying that anybody in the first centuries used to feed people on this occasion (see also Sharing and reading quran
). This means that once we established a "sunnah" (in Arabic a path or something to follow) that says we should feed people at each khatmah we will be committing an innovation in the religion and that is bida'h.
So basically taking the opportunity of a Khatmah to feed people, who are around you or visited you is a good deed, but establishing it as a custom, and doing it deliberately at each khatmah and asking or inviting people to do so will be a bad deed and a bida'h.
(This is also the conclusion of these two fatwas in Arabic on islamweb #125296 and #64591)
So it seems a rather cultural thing, may Allah forgive them:
And [there are] others who have acknowledged their sins. They had mixed a righteous deed with another that was bad. Perhaps Allah will turn to them in forgiveness. Indeed, Allah is Forgiving and Merciful. (9:102)