Trying to pitch the Fediverse on its technology backend to non-technical people is a bad approach, but so is trying to pitch it in terms of digital detox or "better" culture.
The backend is for the tech people, and the rest is your regular messy people. There are as many good pockets of the Fediverse as bad, because that's the internet.
In light of that, it's questionable to what extent the Fediverse should be pitched as a distinct thing in a similar vein as those platforms some Fediverse software emulates. Fediverse, open social web, whatever you want to call it is of main relevance more to those working on it and trying to promote it among developers.
To those of us using these platforms, it's probably better to simply invite those to our respective instances/sites as simply another site/app without all the jargon and background.
Forget Lemmy/Mastodon/Pixelfed/etc. except insofar as it's in the URL or needed to search apps. Ultimately they're backends, and many weren't going around inviting people to their sites or enthusiast forums talking up apache or phpbb or the like.
The Fediverse is an emerging subset of the open web with improved interconnectedness, and so what's more important than it is reinvigorating the spirit of the open web by reminding people there's more beyond the closed web by inviting and encouraging them to visit our open spaces alongside their own. It's closed web/walled garden thinking to discourage visiting a variety of sites and using a variety of apps.
The open web thrives, enduring, enveloping and eroding the enclosures despite their efforts to ward off its persistent being.
TL;DR:
Invite people to these spaces without the technobabble, don't give them shit for visiting/using enclosed sites/apps.
Celebrate the open web by showing them more places online to check out alongside theirs.
You might try copy and pasting the link into your instance's search bar to try to get it to fetch/sync the post so that you may reply to it. That's how it generally works in my experience when running into your situation, supposing your instance isn't defederated from the other person's.