Copy-paste between Hyper-V guest and host

You can use ncat - which also has a windows port - to transfer data over network. On one system you run it in "listen" mode, where it binds to some port, on the other system you connect to that port on the other machine. This creates a bi-directional pipe. On Linux you can choose from more variants (GNU netcat, BSD netcat, socat...). Apart from the obvious man page, you can also have a look at the wikipedia netcat article.

Note: on both systems you run these in the terminal (Windows command line, Unix shell) - the copy-paste has to happen twice: on one machine you copy from the source and paste it into the terminal which is running ncat. The data is transferred to the other machine, where you copy it from the terminal to its final destination.

Other option is to exchange files over a Windows share (Samba on Linux).