Sounds like the flex-to-glass tabs that connect the LCD driver PCBs to the LCD glass itself. If you remove the frame so you have access, you should find that applying pressure to the tabs where they're bonded to the glass resolves the problem. A simple fix is to apply pads over the tabs, to give an even pressure constantly, between tab and frame.
Other than that, you'd need to rebond using anisotropic glue or tape and hope to align perfectly. There are rebonding machines, but they're very expensive.
