Word for "when someone does something good for you and then mentions it persistently afterwards"

It depends on the gift giver's intent, but could he have been "holding it over" you or "lording it over" you?

Either way, he "never let you forget" that he once gave you that gift. And you may "never hear the end of it."

Milked it for all it was worth

Free Dictionary definition

never let them forget it

E.g.:

John once drove Jane to the airport as a favor, and he never let her forget it. Just the other day, twenty years later, he asked Jane to get him some coffee; saying, "Remember when I drove you to the airport? The least you can do is get me a cup of coffee."

You could use "bring up" in conjunction with "broken record" -

Bring [something] up:

To mention someone or something in conversation. A noun or pronoun can be used between "bring" and "up."

A broken record:

a damaged record that repeats part of a recording over and over again —used figuratively in describing something (such as a statement or experience) that is frequently or tediously repeated

For example,

A bought a present for me and then brought it up on every occasion [like a broken record]..

Here's something else you can use -

Labor the point:

To talk about or emphasize something excessively and perhaps repetitively, usually to the extent that the listener becomes bored or annoyed.

If someone labours the point, they keep explaining something or emphasizing a fact even though people have already understood it.

A: "I don't mean to labor the point, but I'm just worried that there won't be enough food at the party."

B: "Yeah, we know, you've said that 10 times now."

For example,

A bought a present for me and then labored the point on every occasion..

I also found a [Latin] phrase that could possibly fit in your scenario -

Ad nauseam [ad naw-zee-uh m]

used to refer to the fact that something has been done or repeated so often that it has become annoying or tiresome.

(Lexico)

Ad nauseam is a Latin phrase that literally means “to nausea”.

Use ad nauseam to describe something that’s been repeated or discussed so long that you’re sick of hearing about it.

(Grammarly)

: so many times that it annoys people.

(macmillan)

For example,

A bought a present for me and then brought it up ad nauseam on every occasion.