The current downloaded Recuva installation file, from both Piriform and FileHippo, is called version 1.43.623 on their websites (although the installation file itself is labelled Version 1.0.0.0).
When Recuva is installed from the FileHippo download, however, the version number of recuva.exe in C:\Program Files\Recuva is 1.43.0.623.
The situation is unchaged when I uninstall Recuva, delete the directory C:\Progrram Files\Recuva, and then reinstall Recuva from the Piriform download.
FileHippo is still complaining that Recuva needs updating --- it says that Version 1.43.0.623 is installed, and that I should update to Version 1.43.623.
Clearly there is confusion about the number of the current version, and FileHippo is misreporting the need for an update. I have emailed FileHippo, but they do not reply to emails, and the situation with their website is uinchanged after two days. Because re-installation using the download from Piriform involves exactly the same confusion, it seems to be Piriform's responsibility to resolve the problem.