If in doubt, take an automatic dot punch to it.
LV are among the better insurers out there.
The questions, or rather overseeing, you should do are gel pack refitment (better to get a new one) and competent application of the urethane glue. All too often they rush it and leave a gap in the glue bead, and it's misty windows time the following morning.
If you're feeling flush or if the insurer will sign it off (rare), get a genuine screen. Aftermarket replacements are brittle and thin.