Can ISP see what I surf on Remote computer?

I have a question about how VNC Connect works. I currently use this program to monitor Desktop "H" when I can't physically be in front of Desktop "H", but this is my question, and it a little techy.

If I'm physically on and in front of Desktop "G", I am aware that everything I do on Desktop "G" can be monitored through the history in the browser and my internet service provider ALSO is aware of every site I visit. If I use Desktop "G" to access Desktop "H", with VNC Connect , does my internet provider have access to what I surf on Desktop "H", even though Desktop "H" is not physically at the same site as Desktop "G"?

Basically, I want to be able to use Desktop "G" to access Desktop "H", and surf freely and privately, but because I don't understand the tech behind the app, I don't know if I am really surfing privately. I hope you understand the question, and thank you in advance for your answer and help.