letterhead required for recommendation emails sent electronically? I am applying to graduate schools in North America. Most of these institutes require at least three electronic letter of recommendations to be sent during the process.

I have already submitted my application to two universities, with the LORs submitted electronically using official email IDs of my professors (including one who primarily works at another university, and was an adjunct professor to me). But all of my professors submitted these without letterheads.

I have checked the Graduate Admission FAQs of most of these university and letterhead is stressed only for hard copies sent directly to the institute (i.e. there is no mention of a requirement for electronic LOR). How relevant is it for letterheads to be attached to the electronic LORs too?

Should I email every institute I am applying to, to clarify this requirement, or just let my professors know that submitting them as is, is fine? It may be worth knowing I am an international student.
I would not worry.  It's traditional to use letterhead for electronic recommendation letters, but it's not really essential.  The admissions committee is very unlikely to care whether letterhead is used, and it should not have any effect on their decision.  In the unlikely event that they have questions about the letter's authenticity, they would contact the writer directly (e.g. by looking up their contact info on the university's web site).

If they haven't sent the letters yet, you could let them know that letterhead is customary and suggest that they use it if convenient.  If the letters have already been sent, then I'd just ignore it.  It's not worth the trouble of resubmitting.