There is a video at https://www.youtube.com/watch?v=gAk6fBY0L3s&t=5s called Ag cur tú fein in aithne - Introducing Yourself on the Gaeilge go Deo Youtube channel.

I don't think the girl there knows much Irish. I pointed out in the comments it should be "do do chur féin in aithne".

She pointed me to links on teanglann.ie and focloir.ie giving "duine a chur in aithne do dhuine" and "ar mhaith leat tú féin a chur in aithne?" She fails to realise that these are not example of the "ag cur + pronoun".

There is a difference between "é a dhéanamh", "to do it" and "á dhéanamh", "doing it". You can't say "ag déanamh é".

And yet she pointed me to materials by TEG Teastas Eorpach na Gaeilge for its A1 (most basic) level of Irish at https://www.teg.ie/home/%C3%A1bhar-teagaisc.291.html There is a document there on that page called "05. Ag cur tú fein in aithne (Labhairt)".

It's odd that the very people who are in charge of testing Irish promote the wrong thing.

Ag cur + pronouns

Ag cur +mé= do mo chur
Ag cur +tú= do do chur
Ag cur +é=á chur
Ag cur +í=á cur
Ag cur +sinn=dár gcur
Ag cur +sibh=do bhur gcur
Ag cur +iad=á gcur

This does seem odd. The woman from the video appears to be going off of some book or something, so I wouldn't automatically assume that she has a deep understanding of what she's teaching. As for the document, I found other mistakes, namely writing Cé tusa instead of Cé thusa, which I would expect from the Caighdéan. Perhaps they are wrongly simplifying the resources because they assume that the real grammar would be 'too complicated' for new learners, or perhaps they just don't have a deep understanding of the grammar themselves.

Well, a lot of things produced by the L2 speakers who control the language contain mistakes. The Turas Teanga book has "conas mar" throughout where "conas" would be advisable (there is a difference - conas mar is for indirect questions). Cé hé thusa? is what I'm familiar with from Muskerry sources. Cé hé me? Cé hé thu? With a mandatory hé in there. And cé hé féin? in the third person. And Cé hiad sinn-na? Cé hiad sibhse? and Cé hiad féin? in the plural. There are probably dialectal differences in this area of grammar.

Do do chur - this is Standard Irish. I don't know of any part of the Gaeltacht that says this.

"Ad chur" is what is found in Muskerry literature (ag+do+chur), but we have discussed on this forum many times the debate on whether "do" or "ag" should be used in such phrases, and is seems there is no difference. This is why in my published words, it is " 'od chur", which implied do+do has been reduced to 'od. In any case the important thing is the pronunciation: schwa+d.

The 6 forms are then:

am chur: the "am" can just be a syllabic devoiced m
ad chur
á chur
ár gcur
úr gcur
á gcur

(The verbal noun is frequently cuir, not cur, but this is tangential to this discussion.)

Out of curiosity, I checked Graiméar na mBráithre Críostaí and corpus Foclóir.ie – if there are any hits for stuff like this there.

Not a single one from native speakers, only one possible non-native instance. There were quite a few of the type tá mé ag rá mé féin – but that’s obviously different (‘I am saying myself’, reinforcing the subject, nothing to do with the object), and there was one non-native sample with ag glanadh iad féin which seems to be intended as reflexive ‘cleaning themselves’, though I guess it could also be parsed as ‘doing the cleaning themselves’.

Seeing that the material is A1, I wonder, like Séamus, if it’s not this weird idea of “simplifying the language” (by… making it ungrammatical ) because the correct way hasn’t been taught to the learner yet. (Which is bonkers, but I know that there are people advocating this, and there were full books written arguing for “simplifying the language” for the beginners’ sake, claiming that a learner should first learn an “easy” version and only later ascend to the actual correct usage…).

Well, tá mé ag rá mé féin is clearly Béarlachas, albeit something some younger speakers might say.

Another point: "the king himself". In Papers on Irish Idiom, p38, Peadar Ua Laoghaire wrote: "An rí féin (not an rí é féin)". It is "duine féin", not "duine é féin", etc. I feel this é féin may be spreading from learners to younger speakers in the GT.

PUL also insisted there was no such Irish word as féinmharú. From Notes on Irish Words and Usages p6:

As far as I'm aware, although I could be wrong, the h-é is not required in Corca Dhuibhne, which would make this Cé thusa?, as well as the occasional identical form of second person pronouns for both subject and object forms within sub-dialects, which would indeed make this Cé tusa (but only in certain dialects.

‘Ag cur tú féin in aithne/Do do chur féin in aithne’ -

As a lesson/paragraph/topic heading etc. it would be expressed as ‘Tú féin a chur in aithne’

Yes, you're right. What (in English terms) is the infinitive and not the gerund. But TEG has the form with ag cur tú féin - if you were going to have the gerund, it would be: ad chur féin in aithne. But as you say, it is better in the infinitival form.

I emailed TEG yesterday, and shock! horror!, they haven't replied. They probably don't want to admit that they, the people who do the very testing of Irish, got the basic grammar of the A1 level of Irish wrong.... The good news is that these people draw a public salary - if that is good news. The number of hangers-on in Ireland who draw a living from the CO is amazing.