Since I am a volunteer rosary maker for Rosary Army, which gives away rosaries to anyone who asks, I think I know a little bit about this…
If a rosary has been blessed, it should be given only to a Catholic, or a

non-Catholic Christian like me, who knows how to treat a blessed item.
**As long as the rosaries have
not been blessed, they are not sacramentals, and may be given to anyone, of any faith. If you have any question as to whether the rosary/rosaries may have been blessed, it would be better to place it somewhere in a Catholic church, with the idea that anyone there can take it. (I would say, put a note with it, that it is a blessed item).
This is an important distinction, especially in regard to the kind of rosary that sometimes arrives in the mail…I have several blessed items, or at least, items I am told have been blessed, and I care for them carefully, with the respect they deserve, as such…
Also, as a thrift store shopper, I try to take special care of any rosaries (or other similar items) that come into my possession, assuming that they have been, at some point, blessed. (I know they lose their blessing when sold, but I still think extra care is a good practice)…
And there may very well be Catholic ladies among the women (& children) helped by this group, who may have fled with only the clothes on their back, having to leave rosaries behind. They wouls surely be most grateful for any rosary you might have to give them.
HTH!!