Cardinal Burke, himself, signed the petition. As far as public comments from the good Cardinal, we have haven't heard word one from him since he was recently summoned to Rome for a "private meeting" with Francis.
Why do you think the Cardinal is now silent?
Highly unlikely that the “professional Catholics” at Catholic Answers and EWTN would promote a petition embarrassing to the Pope.
I don’t think he actually signed it. Nor do I think any of the other “personalities” did either.
The whole thing looks like a sham, and there is no independent verification, any where.