Why Did my Doctor Use Steri Strips on Top of my Upper Eyelid Stitches?

Steri-strips are commonly used on the incisions to reduce the amount of tension in the area. Tension can compromise your recovery and make scarring worse. While they aren’t totally necessary, some surgeons still use them in this area. They gradually fall off on their own, but if they're causing you discomfort right now, it’s best to let your surgeon know so they can suggest something to help you.

The steristrips can help keep the incision line sealed, minimizing tension on them. You should ask your surgeon about what to do.

I would certainly address your question with your Surgeon.  Steristrips are used for two reasons 1) reduce wound tension, and/or 2) hold a suture in place. I close my upper eyelid Blepharoplasty incisions with a running subcuticular prolene suture.  In this situation, steristrips are used to hold the ends of the suture in place and prevent inadvertent removal; the suture is gently pulled out of the healed incision a week later.  For this reason, I do not recommend placing ointment on steristrips