Hmm, same as with most other terminal emulators, even without pressing Ctrl+Shift+V,Termite. It doesn't seem possible to select any of the text output within for copying.
drag-selecting some text should cause that text range to become the "primary selection".
I would expect either of the following to accomplish pasting:
1) drag-select a range of text in termite
2) focus another application window and press Ctrl+V (or right click and use the applications's context menu Paste action)
or
1) drag-select a range of text in termite
2) press Ctrl+Shift+V
3) focus another application window and press Ctrl+V (or right click and use the applications's context menu Paste action)
Finding either of the above to be unsuccessful, I would purge/reinstall termite and/or check whether a global (xfwm) keybind is trapping Ctrl+Shift+V