We redeemed a scratch off ticket lottery with the Texas Lottery Commission we got from the bad girl with our EIN. The state took 25% off the top of the winnings. Is their anyway for us to get back the taxes paid because we are tax exempt? Scratching my head!

Not likely - the purchaser (presumably the bad girl) was the actual winner, and she owes the tax. Similar to having a defendant surrender (endorse) a paycheck to you - and trying to claim that the withholding, etc. should not be withheld since you are tax exempt. My 2 cents.