David,
I suppose if it were me, I would be willing to knock a bit off my original bill if I was assured that the other abstractors work is being relied on.  Having no liability on the work would be worth a bit of a discount.
The think that strikes me as most odd is the client also ordering from the other abstractor without noticing it had also been sent to you.  It seems they should have noticed, and called one or the other of you right away.
Best of luck,
Doug