Not in the habit of submitting manuscripts, I can only guess -
editor invited No one has yet read the MS, but eligible people are solicited to do so.
with editor The MS is currently in the possession of an editor.
Technical Check In Progress The MS is being edited for factual accuracy,
OR the grammar, punctuation, spelling etc. are being checked.
Edit. A. S.'s reply seems more authoritative: eg, "
reviewed for factual accuracy" would be better than "
edited for factual accuracy," etc.