Yes, "At your help" is grammatically incorrect. And goofy sounding.
That said, if you're just starting the job and they're paying your salary, I'd say whatever silly thing they tell you to say. When you've been there a while and you have some credibility might be a time to complain about the patter.
People don't listen to what you say when you answer the phone anyway.
At a job I had a few years back, we had a phone line installed that was only used for the computer to make outgoing calls. The phone number was not published or given to anyone because there was no reason for anyone to call. One day I was standing by the computer when the phone rang. I hesitated a moment, then picked it up and said, "Hello, wrong number."
The person at the other end just went right ahead and said, "Can I speak to Fred Jones?" or whatever the name was.
"No," I said, "This is the wrong number."
"Is this XYZ Company?" he asked.
"No," I repeated, "You have the wrong number."
He wasn't listening to anything I said at all.