UPDATE dbo.tblCustomer
SET Extra=NULL
FROM inserted tI
WHERE dbo.tblCustomer.CID = tI.CID
-- Worth checking for non empty?
AND dbo.tblCustomer.Extra <> ''
If you want the column to be set always to null, then you shouldn't be checking for an empty string.
'' is not the same as null.
Null equivalent would be
AND dbo.tblCustomer.Extra is not null