You could use the smbclient command (part of the Samba package) to access the SMB/CIFS server from within the Docker container without mounting it, in the same way that you might use curl to download or upload a file.
There is a question on StackExchange Unix that deals with this, but in short:
smbclient //server/share -c ‘cd /path/to/file; put myfile’
For multiple files there is the -T option which can create or extract .tar archives, however this looks like it would be a two step process (one to create the .tar and then another to extract it locally). I’m not sure whether you could use a pipe to do it in one step.