If they were aware of your prices at the time they ordered your services and/or they agreed to your prices either expressly or implicitly verbally or in writing and/or they accepted your services with knowledge of your prices, they are contractually bound to pay you the agreed price.They can not unilatterally reduce the price.

If any of the above are true, you have potential claims against them for contract breach (express or implied) and for unjust enrichment. If your state has an unfair trade practices statute, you may also have a claim against them under the statute also. Most unfair trade statues provide for recovery of attorney's fees and in some cases double or tripple damages. You should consult a local attorney immediately.

If you intend to make an issue of it, do not cash the check you received from them. It gives rise to a defense called Accord and Satisfation (settlement). If you cash the check or deposit it, they can argue that you agreed to settle your claim for the lower amount.

Did they include the price of the search on the order? If it differed from your price, and you performed the search after you received the order, it could be argued that they made a counteroffer to your price. They could then argue that your performance of the search after receiving the order with the reduced price constituted an implied acceptance of their counter offer.

Which company created the problem?