I'd be annoyed by that mnemonic - lazy, thoughtless, everyday sexism, potentially upsetting to anxious teens.
I think my dd would probably have called the teacher out on that one - I generally tell her not to argue with teachers even when she disagrees with them, but was proud when she pulled a supply teacher up for telling a boy to "stop acting like a girl".
Nothing wrong with mnemonics being silly or rude - that makes them more memorable.
But I do think mnemonics need to be limited to words that could trip you up eg by having to remember which letters are doubled and which are not such as "1 collar and 2 sleeves" for "necessary".
If somebody finds spelling difficult then I think that it's more helpful to try and develop additional strategies. If you rely on mnemonics for every word then you'd have far too many to remember.
OP, August is phonetically regular so I'd get your son to use phonics. Break the word into syllables by saying it out loud and clapping it. For the first syllable either remember that it's one of the ways of writing the "or" sound or use the letter names and think of it as "Eh you!".
For the second syllable, sound it out: "g-u-s-t-gust". Say it out aloud over and over again, "counting" each sound by starting off with hand made into a fist and then sticking out a finger each time you say a sound.