Exporting your reviews
The short answer
There is no option to export or download the reviews from a widget. It is a frequently requested feature and it is on the wishlist.
Reviews collected from a platform still live on that platform, where the platform’s own export options apply.
Why people ask
Usually one of three reasons: moving to another tool, analysing what customers say, or keeping a record before a platform removes something. The first is the most common and the least served by an export, since the reviews would be re-collected from the source anyway.
What you can do
Reviews collected automatically remain on Google, Tripadvisor and the rest, and Google Business Profile has its own export. For manually added reviews, the text is in your widget settings and can be copied out.
For bulk work in the other direction — getting many reviews into the widget — support can upload a CSV for Pro and above.
If you need it
Vote on the wishlist. Feature priority there is genuinely influenced by volume.