First of all, any unclaimed property may be claimed without the help of a third party. The Harris County Tax Assessor allows one to easily request the refund without use of another company. See HERE.
Second, because there is no need to pay the third party and one would be paying at their own discretion, and because someone in your situation would essentially be getting the money back and thus "made whole," there is damage/injury.
An analogy may be this. I loan you my bike but instead of bringing it back, you leave it near my home. It is not damaged, but I have to go get it - which I do. I got the bike back without a scratch, I am "whole," there is no case. Had I needed a tow (equivalent to your third party), I can sue for the tow's cost, but I do not need it since the bike is right near me and has keys in it.
As such, this would be a weak case.
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