Am I replacing the iMac screen properly?

I removed all the adhesive around the outside of my iMac screen. Below the foam adhesive there also seems to be a line of black adhesive almost like electrical tape. Is it OK to remove this as well? It appears to be what the adhesive tape was sitting on. Don’t wanna replace the screen and find out that tape never should’ve been removed. Thank you so much for your responses.

Unfortunately, It’s off on one side. Should I remove it from the other side, try to replace it, or just let it go and continue with adding the new adhesive strips to both sides? All four sides ARE free from any old adhesive, I’m just making sure the new adhesive strips are designed to stick to the clean bare metal frame. Thank you.