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The thin rubber strip surrounding the front display got out. I pushed it in, but it didn’t be fixed. Do I need to buy new display and replace it? or I can fix it?

This model uses a plastic bezel which you can replace following this IFIXIT guide: MacBook Unibody Model A1342 Front Display Bezel Replacement. I would recommend getting this tool kit: iOpener as you’ll need the picks and cards to hold the bezel way from the glue as you use the iOpener to soften the glues adhesion. While you might think you can be a little ruff in taking it off as you’ll be replacing it you still want to use some care as you can damage the display if you are not careful. Here’s the replacement bezel Genuine Apple MacbooK 13" A1342 2009 2010 LCD Front Bezel