Translation:Scríobhann an dalta an tuairisc faoi threoir an mhúinteora.
It's the genitive case. threoir an mhúinteora is one thing, similar to "the teacher's guidance". Also, that's the only reason múinteora is lenited - in the genitive, after an masculine nouns lenite.
Go raibh maith agat! I didnt think to look at it that way! does this mean that "muinteora" is more like an adjective rather than a noun?
In this sentence, yes. Irish uses genitive nouns as adjectival modifiers more often than English does, e.g. turas scoile (“school trip”), teach tábhairne (“pub”, literally “tavern house”).