Installation failure with error message about duplicate DB column

I have cleaned JFBConnect out of the database numerous times, including the extensions table and still get the same error:

JInstaller: :Install: Error SQL Duplicate column name 'params' SQL=ALTER TABLE `#__jfbconnect_user_map` ADD COLUMN `params` TEXT;
Extension Install: SQL error processing query: DB function failed with error number 1060
Duplicate column name 'params' SQL=ALTER TABLE `#__jfbconnect_user_map` ADD COLUMN `params` TEXT;
SQL =
ALTER TABLE `#__jfbconnect_user_map` ADD COLUMN `params` TEXT;