What is the ruling on a teacher increasing students' grades in exchange for memorizing prophetic hadiths and reciting them among themselves, and is this considered by the student as seeking worldly gain through religion?

There is no harm in memorizing hadiths to earn grades, because seeking worldly gain does not preclude seeking heavenly reward. Nor does it prevent a teacher from encouraging students to memorize hadiths by promising them grades, if the regulations permit that.