Small Claims Court in New York City for example has monetary jurisdiction up to $5,000 however before you jump the gun you should be confident that you are right and entitled to the return of the escrow money because if you have a weak case and go it alone without proper legal representation you not only risk losing but your damages could compound themselves in a counter-claim.
Provided that what you said is correct, as to who her share should "pass on to". Keep in mind, if she left a Will then this would govern who takes. If not, then the laws of intestacy would govern. It is a good idea to "confirm" the rightful owners by virtue of a Deed, but be certain that the rightful owners are just that: "the rightful owners".
I really doubt that he can claim anything. Except, however, if he can establish that the payment was somewhat in the form of a loan, and not a gift, he may be able to seek re-imbursement for the payment that he made, since it appears from the question that he had no legal obligation to make the payment.
Although I note you are in California, if the law is similar to that in New York, what you are referring to is a "quitclaim deed". You stated that the Deed is recorded so as such, it is now a public record and is readily accessible by anyone as being a "public record". So while his daughter may easily obtain a copy of the recorded Deed directly herself without the need for your intecession, you can, easily enough, provide her with a copy as a courtesy in that you will be providing her with...