For Delete trigger with condition on a joined table
Have you tried:

CREATE TRIGGER [dbo].[bwrTriggerAuditRecord] on [dbo].[Borrower]
AFTER DELETE AS
INSERT INTO AuditLog (TableName,TableID, DeletedOn)
SELECT 'Borrower' AS TableName ,
       i.ssn,
       GETDATE()
FROM deleted i
join filedata fd on (i.FileDataID = fd.FileDataID )
INNER JOIN (select OrganizationID from Organization where code not like '26%') org on (fd.OrganizationID = org.OrganizationId)
where fd.filename not like '26%' 
and fd.filename not like '%.copy' and fd.filename not like '%+'


You shouldn't need to tie back to the Borrower table - the deleted table should hold all the same columns as Borrower did.