I figured it gave the option to either play quarter notes or half notes, but it did seem oddly unspecific. What was it they wanted her to play?
Hard to tell. Probably an artifact from the original creation process. Almost certainly ignorable.
Musical theater is not written in the way that most other music is. With most types of music, a composer writes it all first in all of its detail, and then the performer(s) perform it as-is. With musicals, the inaugural production starts rehearsals with something far short of a final draft, often loose piano sketches. Throughout the production process, music is added, cut, and rewritten all the time, even into performances. In most cases, a separate orchestrator is responsible for taking these hastily written sketches and converting them into playable orchestra parts, and there are probably many copyists assisting in typesetting parts. There's a lot of communication that needs to happen between these people, and some of it takes place via written notes in the materials. Sometimes we see artifacts of these conversations in the final product.
I think that's what we see here. Given that the surrounding music is in half notes, I suspect that an earlier version of mm. 121-122 was in half notes, then at some point someone thought, "hmm, maybe that would sound better as quarters" and wrote that note, later someone thought, "yeah that's a good idea" and changed the music but didn't erase the note, and even later someone was typesetting the parts, didn't know what the note meant, and left it in out of caution.
"Maybe quarter notes" means exactly that: consider playing 4 equal-length notes per bar. You'd think this is what is written anyway but it isn't: note that the movement is under the tempo designation "Double-time swing feel (in 2)" which means that 4 notated quarter notes should usually be played as triplet-half triplet-quarter triplet-half triplet-quarter.
This instruction suggests omitting the swing feel for those measures. How this will then fit up with other parts depends on the notes there: my guess would be that there are mostly sustained notes in the melody part.