If one gave their daughter away, wouldn't one have to be a "biological" connection to the daughter. Gifts are to be enjoyed, by all those who perceive it as such. If the other "connection" values the "gift" more, why not return the "gift" to those most appreciative.
There is nothing wrong or even illegal about what they are trying to do. If they want their daughter back, then they are legally allowed to make any and all efforts to get her back. Talk to an attorney for professional legal advice.
Your wording is confusing however the party can raise money within legal means. The case for legal custody will be addressed by lawyer, case worker,agency, and depends entirely on individual situation.