Signed-in members can comment on your events (on the public event page) and on posts in a group's feed. Comments on events appear immediately by default; they are not held in a queue for you to approve first. Blog posts do not have comments today.
Why immediate
A comment held for approval is a conversation that never happens. By the time somebody gets round to approving it, the moment has passed and the person who wrote it has concluded their church does not want to hear from them.
Only signed-in members can comment, so this is not the open internet. The people commenting are people you know.
Dealing with one
Open Comments to see event comments. The Pending tab shows ones waiting for a decision and All Comments shows the rest. Each comment has Approve and Reject.
Two further buttons work on the person rather than the comment: mark as trusted (all their future comments appear without review) and revert to moderated (their future comments wait in Pending until you approve them). If you remove a comment from someone, they are moved to moderated automatically, so one bad comment does not repeat.
A comment is rarely the real problem
Before removing something, consider whether the reply is the better move. A member who commented something sharp about a decision is usually a member who wants to be heard, and silently deleting it confirms whatever they were worried about.
Removing without a word is right for spam, abuse, or anything about a named person. For disagreement, it usually is not.
Reporting is a different system
Members can report content from the mobile app, but reporting covers group chat, direct messages, prayer requests and other members. Comments are not part of it. The app also shows Report on group posts and comments, but those reports don't reach you yet.
So a member who objects to a comment can't flag it to you; they have to tell somebody, because "why did nobody report it?" has an answer, and it is not that nobody minded.
Reports that do come in (with reasons like spam, abuse, or self-harm) land in Moderation, which is a separate queue from this one. A self-harm report in particular is not a moderation task; it is a pastoral one, and the fastest useful response is a person rather than a button.
Who can comment
Settings → Activity Permissions has a Comments row with three levels: Public, Members and Staff only. There is no setting that switches comments off entirely. Staff only is the closest: only editors and admins can then comment. The setting covers comments on events; comments in a group's feed follow the group's own settings.