You need to resolve the discrepancy. Find out which one is right, the flood determination vendor or the appraiser. If the flood vendor is right document the file and move on. If the appraiser is right, you need to go back to your vendor and ask them to review their determination. The determination is ultimately on your bank.
If I find discrepancies between the appriaser and the flood determination, I check it mayself using FEMA's map service center and the county GIS website (which include flood map overlays).
Generally, I have found that appraisers are usually incorrect; HOWEVER, I have had instances where the appraiser was right and the flood vendor was wrong. The big flood vendors yield determinations based on geocoding (ie instant determination), and only actually look at aerial maps with overlays when you request a manual review.
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I can't herd the cats anymore, so I just set up the electric fences and let them fry when they stray out of bounds.