If English is not your first language I would understand your complete ignorance to how it works.
In this context, the use of they are a pronoun is grammatically correct.
“The customer forgot his umbrella in the restaurant. They are coming back for it.”
You guys are as triggered as the gays.
That works for the generic customer.
But it reads less well to say: “Sally forgot their umbrella in the restaurant. They are coming back for it.”
That's very forced and artificial. The words "she" and "her" are OK. We can use them.
Why is a plural pronoun acceptable, when the subjective noun is not specified? I personally write likewise.