Question for the BP populous:

Situation - My wife and I recently purchased an off-market SFR with tenants in place. During the appraisal process for the mortgage, it was identified that the home was actually 218 sq ft smaller than County Tax records indicated. Property Taxes for the house (based on the erroneous home size) are $4,280 this year.
1) In hopes of reducing the property taxes, Is it worth it to update the County's records to reflect the 218 sq ft smaller home size? 2) How do we go about making that change?

Background - It's a 3 bdr /2 ba /2 car attached single story home reported at 1,630 sq ft. built in 1982 in the San Antonio, TX area. Initial sales price from seller was $188,000. Appraised value, with measured home dimensions of 1,417 sq ft, was reset to $175,000. We bought at that price.  

We'd appreciate any guidance as to how we should (and if we should) go about updating the County Records. Thanks for your time!