They can't do a damn thing about it, I wouldn't worry in the slightest. Lying over quals is a no-no for obvious reasons, but it's 100% their choice on what they want to pay you. The fact you're going back and asking for more, i.e. you're not telling them to match what you have now, just puts the ball even more in their court.
I wouldn't worry about it in the slightest.