Ahhh wait a minute... I just saw that your server hasn't updated to the current version of Mastodon that allows quoting.
However, it might have a general setting that allows other people to quote you, which was a temporary stop-gap when the developers first started testing quoting.
If the setting is there, it would be under ⚙️ Preferences > Other > Who can quote, you can switch it off by setting it to "just me" and then saving changes.