Maybe the idea is that the wild male mosquitoes will mate with these sterile, genetically-modified females instead of with some of the wild female mosquitoes, and so the total wild mosquito population will be reduced.

The article doesn't really explain, but there's more to it than that. My guess is that the male offspring are still fertile, but carry the gene drive and so spread the infertile-female gene to all their offspring. Eventually, the entire population is rendered either male or infertile females and dies.

*it's also possible that at the end the males will start hybridizing with females from other species.

Next sentence:

As more and more female mosquitoes inherit two copies of the modification, more and more become sterile.

So maybe the mutations activate only when inherited from _both_ parents?

You may find the details of how this works in the original paper:

https://www.nature.com/articles/nbt.4245