The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.

Optimal indexes for this query:

CREATE INDEX products_idx_uniqueid ON Products (UniqueID);
CREATE INDEX zamcustomer_staff_idx_uniqueid ON ZAMCustomer_Staff (UniqueID);
CREATE INDEX zamkannchanges_idx_actiontype ON ZAMKannChanges (ActionType);
CREATE INDEX zamrentalgarments_idx_uniqueid ON ZAMRentalGarments (UniqueID);
CREATE INDEX zamstaffrentals_idx_uniqueid ON ZAMStaffRentals (UniqueID);
CREATE INDEX t_garment_idx_idgarment ON dbo.t_ProcessIT_Garment (IdGarment);

The optimized query:

SELECT
        kg.IdGarment 
    FROM
        Products p 
    INNER JOIN
        ZAMStaffRentals r 
            ON r.ProductID = p.UniqueID 
    INNER JOIN
        ZAMCustomer_Staff s 
            ON r.StaffID = s.UniqueID 
    INNER JOIN
        ZAMRentalGarments g 
            ON g.StaffRentalID = r.UniqueID 
    INNER JOIN
        [REMOTE_SERVER].[REMOTE_DB].dbo.t_ProcessIT_Garment kg 
            ON g.BarcodeRFID = kg.IdGarment 
    INNER JOIN
        ZAMKannChanges log 
            ON log.GarmentID = g.UniqueID 
    WHERE
        log.ActionType = 'I'