This is a contract drafting question at its core, so I want to flag upfront: the specific language you use in an agreement should be reviewed by a real estate attorney in your state. What I can do is explain how the fee structure works conceptually, so you know what to ask for.
The problem here is that the fee was tied to the deal price rather than the introduction. When a deal renegotiates, a price-tied fee moves with it. The fix is to anchor the fee to the referral event, not the closing number.
Language that does this typically reads something like: "A fee of $X is earned upon introduction of the seller, defined as the investor's first direct contact with the seller, regardless of the price, terms, or structure of any subsequent agreement."
A few things that language needs to do:
Define "introduction" precisely. Name the date, the seller, and the property address. The moment that introduction happened, the fee is earned. What closes after that is a separate matter.
Separate the trigger from the amount. The fee triggers on introduction. The amount can be fixed (a flat $2,000, for example) or calculated from the original submitted offer price, stated explicitly as the price in the bird dog's written lead submission, not the final closing price.
Include a direct-contact clause. This says the investor agrees not to contact the seller directly except through channels the bird dog controls, until the fee agreement is signed. Once they have the seller's number, your leverage is gone.
The thing worth knowing here is that verbal agreements and informal handshakes are how bird dogs get burned most often. The agreement needs to exist in writing before the introduction happens, not after.
What did your original agreement look like? Was anything in writing before you handed over the contact?