To be honest I've never attempted a rear glass replacement due to the difficulty, messiness and potential for damage to other components. But it's my understanding that the goal is to remove all the glass and adhesive in order to provide a clean surface to mount a new piece of glass.
It looks to me like you've only got half the job done; you've done a pretty good job of getting the glass off, but virtually all of the adhesive is still in place. I would suggest that you need to get out a hot air gun and blast the heck out of the glue that's still on the screen and scrape it off when it's softened. Once all the glue is gone, the glass shards you're concerned about will be gone as well.
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