I would get another cushion insert- try contacting a professional upholsterer- and toss the one that got peed on. Then I would follow manufacturer directions on cleaning the cover.

The smell of urine may not be noticeable to you but dogs can smell it regardless. In short it will never be "urine-free" but the cushion would retain the most odor despite any cleaning.

Dogs have between 150-300 million scent receptors that can detect scent concentration up to 100 million times lower than human detection. Since you foster animals- this one incident can spark future (or current) furkids to mark the same spot.