As a relay operator for
IP-Relay.com I can give a few hints and maybe some insight on what happens.
First of all, unless we're instructed by the text user (you) we cannot tell the called party that you are deaf/HOH/speech disabled. It is against the rules.
We do try to do our best to make sure the called party stays on the line, we make sure they know it is not telemarketing if they ask, we say something like "no sir/ma am you're receiving a call from someone using the relay service" or.. if you give us permission upfront to tell them we can say "you're receiving a call from a person who may be deaf, hard of hearing, or speech disabled."
How the call goes really depends on how much instruction you give us (oprs).
Remember, you can tell an opr to announce a call a certain way, you can tell us not to announce or explain relay, or use any of the GA/SK protocol.
I am here to try to do my best to help people who are frustrated with the relay service, if anybody here thinks I shouldn't be here or offer help just let me know and I will disappear.