They sing the song once it's been decided that Dorothy & Co. will in fact get an audience with the Wizard. Then everyone is like, "Hey you guys are a hot mess and we can't let you see the Wizard like that. Let's go to the Wash & Brush Co. where they'll clean you up." When they get to the Wash & Brush Co. the facility seems tailor made for a girl, lion, tin man and scarecrow--like those are the only demographics served at the establishment. The disturbing part is when they're working on Dorothy.
Wash & Brush Co. Girls: We can make a dimpled smile out of a frown
Dorothy: Can you even dye my eyes to match my gown?
Wash & Brush Co. Girls: Uh-huh
Dorothy: Jolly old town!
I'm not even going to ask how they make dimpled smiles out of frowns. Had they sung that to me, I would've been concerned. But not Dorothy. Dorothy says, "Hey, while you're at it, how about dying my eyeballs?" What's up with that? Had the movie been made in 2011, Dorothy could've just asked for some colored contact lenses. But the movie was made in 1939 and I'm pretty sure that contacts (or at the very least the colored ones) weren't a thing.
Why was that the lyric they went with? It wasn't like this was based on a true story and they wanted to maintain some sort of integrity. It's just a line in a musical. We could've dyed her socks to match her gown or something normal. But no, we dyed her eyeballs. I would think that, had that happened, Dorothy would've had bigger problems than just getting back to Kansas. Uncle Henry and Aunt Em would have been supporting her all their lives because she would've been blind.