You give them the credentials for your Apple account. The security concept is “trust me bro” and that’s really the best they can do unless Apple helps them (which they have no reason to)
“Trust me bro” is always the security concept of any service where you don’t control the client - that includes regular iMessage (you have to trust Apple) and Google’s RCS (you have to trust Google). They can always instruct or update the client apps on people’s phones to start doing something they weren’t previously doing.
That being said, I would not trust some random sketchy company with something so important. Even if you trust their intentions, you cannot trust their competence in preventing breaches. Stuff gets hacked and leaked all the time.