The grammar problems Nelda points out to Bud with his use or misuse of relative pronouns are examples of the notorious misplaced modifier.
The first line of the episode is Margaret telling Bud she had a talk with the Dean of Men at the college about Bud's grades. Bud and actress Diane Millay, are portraying college students, not high school. Ms. Millay's age of 26 and Billy Gray's 22 are consistent with college students.
Bud's attractive blonde tutor is supposed to be a fellow teenage high school student, but the actress who played her (Diana Millay) was actually 26 years old when this episode was shot.