At least it wasn't due to Gronkowski possibly hiding anything.
His 4th arm surgery would be to change out the hardware, which would have been contaminated by his previously treated pus draining infection. However, if the bone infection (osteomyelitis) accounting for the last surgery and antibiotics have not entirely eradicated the infection, they will have to remove part of the infected bone..........wait until the infection is totally gone (and hopefully also delaying placing a new set of hardware [that can again be contaminated by the continuing infection] after removing the existing hardware.......unlike what was done last surgery).........then a 5th surgery to possibly bone graft support the missing portion of bone (if large enough) + or - supportive hardware again (which at one point in time further in the future would then require a 6th surgery for removal of new hardware)...........It all depends on what they find during the 4th arm surgery infection-wise.
Furthermore, if there are any residual signs of infection in the arm, they will not be proceeding with the back surgery. His back surgery will be a minimally invasive disc procedure. Sounds quick and easy, but the recovery is still at least ~5 months. For those that don't remember, he had similar minimally invasive back disc (microdiscectomy) surgery in 2009 and missed the entire season.
I don't envy Gronk.