One of the best features of Mastodon is the lack of quote-tweeting. I'd forgotten how great that was. And unfortunately for Twitter, it's a feature that they'll never be able to copy.
If you're inclined, you can dump the full URL of a Toot into your own Toot; essentially quoting it like any other URL-identified resource. The ergonomics isn't quite "quote tweet" but for occasionally writing a Toot which references another Toot (rather than replying to it), it ought to do the job.
You can't prevent people from quoting you on the Internet such that you don't know about it.