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Persistent yellow or pus like discharge for 2 to 3 months after rotator cuff repair needs proper evaluation. Although sometimes this can be a reaction to internal sutures or anchor material, a deep postoperative infection must first be ruled out, especially since the CRP is still significantly elevated. I would not advise continuing repeated courses of antibiotics alone without identifying the cause.

Yes, debridement is must for complete infection removal

You need to undergo debridement and removal of the sutures as the infection will not settle till then

Persistent pus-like drainage for 2–3 months after rotator cuff repair is not expected normal wound healing and raises significant concern for a deep postoperative infection involving the sutures/anchors or repaired tissues. A reaction to suture material is possible, but infection must be excluded first. The attached CRP appears to be 24.79, which is still elevated; however, the exact interpretation depends on the laboratory units and reference range. Even if the CRP has decreased from 54.7, continued drainage is more important clinically and suggests that the problem may still be active. When infection involves implanted sutures/anchors, antibiotics alone may temporarily suppress drainage but may not eradicate the infection because bacteria can persist on the implanted material. Therefore, the surgeon's suggestion of surgical debridement, obtaining deep cultures, and removing infected/non-essential suture or anchor material is a reasonable standard approach. Whether all implants need removal depends on tendon healing, implant stability and findings during surgery.