SQL Server expensive nested loops join and lazy table spool
I would try removing the OR clause in the join between document and processingentitymapping

You could do that with UNION

SELECT distinct d.documentpath as path, d.documentname as name, d.datecreated as created, pc.DateProcessed
FROM datagatheringruntime dgr 
INNER JOIN processentitymapping pem on pem.entityid = dgr.entityid 
INNER JOIN document d on d.entityid = pem.entityid 
LEFT JOIN PendingCorrespondence pc on pc.PendingCorrespondenceId = d.PendingCorrespondenceId
WHERE rootid = @P0 and dgr.name in('cust_pn', 'case_pn')
UNION
SELECT distinct d.documentpath as path, d.documentname as name, d.datecreated as created, pc.DateProcessed
FROM datagatheringruntime dgr 
INNER JOIN processentitymapping pem on pem.entityid = dgr.entityid 
INNER JOIN document d on d.unitofworkid = pem.processid
LEFT JOIN PendingCorrespondence pc on pc.PendingCorrespondenceId = d.PendingCorrespondenceId
WHERE rootid = @P0 and dgr.name in('cust_pn', 'case_pn')
OPTION(RECOMPILE);


The reason being that the table spool is feeding the NESTED LOOPS operator 


And on this nested loops operator is the OR predicate.


Filtering out until we have 9 rows remaining.  

Changing the OR to a UNION should remove the spool, you might have to look into indexing after removing the OR.

Indexes that could improve performance after rewriting with UNION

CREATE INDEX IX_EntityId
on document(EntityId)
INCLUDE(DocumentPath, DocumentName, DateCreated, PendingCorrespondenceId);

CREATE INDEX IX_UnitOfWorkId
on document(UnitOfWorkId)
INCLUDE(DocumentPath, DocumentName, DateCreated, PendingCorrespondenceId);


See here for another example on this