This is the name of a collection of tactile children's books. In Irish would it be - Teagmhaigh leis agus mothaigh é ?

To say "touch (it)" you could also say "bain dó", it may be clearer than "teagmhaigh".

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Go raibh maith agat, a chara.

I've read "bain do" only in negative sentences.
https://www.teanglann.ie/en/fgb/bain_do seems to support this.
There are only negative examples: Ná bain dó. = Don't touch it.

Ná / bain dó - I'm not familiar with that meaning.
Ná bain dó é - In Conamara that would mean "don't take it off him".
Bain díot do chuid bróga - Take off your shoes.
Ní bhaineann sé leat: It doesn't concern you.

For touch I'd say: Ná leag lámh air. Don't place a hand on it.

This is not a correction, I'm only familiar with my own dialect.