Nothing is FDA approved for reactive arthritis because of a lack of research. Reactive arthritis is rare in the realm of spondyloartrtitis which collectively is more common than RA. Indications for Remacade are the following:

REMICADE® is a prescription medication used to treat:

Crohn's Disease
Pediatric Crohn's Disease
Ulcerative Colitis
Pediatric Ulcerative Colitis
Rheumatoid Arthritis
Psoriatic Arthritis
Ankylosing Spondylitis
Plaque Psoriasis

With the exception of RA, all of these conditions are part of the spondyloarthritis family.
https://www.arthritis.org/diseases/spondyloarthritis