Our County Clerk has filed a certified copy of a probate in the County�s Official Public Records. The documents that were filed accidentally had a settlement statement attached to it that was filed along with the probate. The settlement statement has a social security number on it. The certified copy of the probate (along with the settlement statement) has a Volume and Page number stamped on it. The County Clerk has been asked to remove the settlement statement from the Official Public Records and replace it with blank pages since the settlement statement was mistakenly filed. I do not believe that the settlement statement can be removed because once a document is filed, it is permanently in the records. Is this correct?

You are correct. Once documents have been filed in the county clerk's records, they are subject to permanent retention. I know of no mechanism to remove a filed document from the official public records (except, perhaps, by way of a declaratory judgment and ancillary injunction or mandamus order). The remedy for keeping prying eyes off of the information in question would be to obtain a sealing order under Tex. R. Civ. P. 76a.