Is it permissible for my grandmother, who is over seventy and cannot pronounce the letters "tha" (ث) and "dhal" (ذ) due to tooth loss, to read the Quran? And what if she can only pronounce them with difficulty?

There is no blame upon one who is unable to pronounce some letters when reciting the Quran, for Allah Almighty says: ﴿Allah does not charge a soul except [with that within] its capacity﴾ (Quran 2:286), and: ﴿and [He] has not placed upon you in religion any difficulty﴾ (Quran 22:78). Therefore, one who is unable to articulate correctly due to an accent or a lisp is not to be blamed. Their prayer is valid, and it is permissible for someone similar to them to follow them [in prayer]; because the lisping person who substitutes one letter for another has a valid prayer when leading someone similar to them.