WHERE notes LIKE '<p><em><strong>Item dropped from ESP datafeed and pricing removed from site on %. May still be available.</strong></em></p>'
Note that I put a % in the string.
I don't understand "delete those strings" -- Do you want to replace them with the empty string? NULL? Delete the row containing that in the notes column? Something else? I hope that the WHERE clause is sufficient to get you moving in the right direction.
Note: REGEXP is 'overkill'; LIKE suffices.
If you want to remove the date but keep the rest of the string, then won't this do?...
UPDATE tbl
SET notes = '<p><em><strong>Item dropped from ESP datafeed and pricing removed from site on xxxxxxxxxxx. May still be available.</strong></em></p>'
WHERE notes LIKE '<p><em><strong>Item dropped from ESP datafeed and pricing removed from site on %. May still be available.</strong></em></p>';
(Or whatever you would like to put as a placeholder.)
MariaDB-10.0.5 has these: REGEXP_REPLACE(), REGEXP_INSTR(), and REGEXP_SUBSTR(); but I don't see that they are necessary for your case.