Solid archives are archives where you need to recompress the full archive when you do an add or delete action on it. They are usually smaller than the not-solid variant but require more effort on updating. Users which want to minimize the archives as much as possible tend to use solid archives.
However, I've just tested a solid and a non solid 7z archive and removal works in both cases.
So you should check if you got an up2date 7z (I'm using 7-Zip 22.01) and 7z.exe must be available via your %PATH% environment variable (or you specify the full path to it in compressor settings). If it still doesn't work for you, the archive in question might have a problem, you could try to use the commandline to manually run 7z.exe d -y -ms=off -mx9 archivename file_in_archive on it to see if this is working.