It was a lice comb so probably some sort of prayer/spell/whatever for it to work better. This particular one was ivory so it was for someone wealthy who possibly could have been able to read it. Poorer people would have used wooden combs.

> I then guess this was an instrument for the wealthy

You guessed correctly, per the article: "It would have been like a diamond today, a crème de la crème luxury item. Others likely had lice combs too, but made of wood that would have decayed"

Reads like it might be instructions to me.