Amending a "right to represent" document?

[NewJeffCT]

About a month ago, I was contacted by a headhunter about a job at a large company in the Hartford, CT area. I was interested, but then the job was put on hold...

In the meantime, I was contacted directly by that same company about a better job in a different department. It's not a perfect fit, but I'm interested.

In the meantime, I just got a call back from the headhunter saying that the job he had called about a month ago is now officially open.

However, he sent me a letter that gives his agency the right to represent me for positions at this company. With where I am located at work currently, it is difficult for me to get out to make a personal phone call, and I have no access to my personal email, either.

Would it be okay for me to self-amend this document to add in the line: "Regarding position # XYZPDQ" to the sentence: "...the exclusive right to present and represent me at their client Big Company"

I don't want to lose the chance at either position.