Can companies monitor the personal computers of independent contractors that work from home offices?

I work from home as an independent contractor, using my own personal computer and my home internet connection, that I pay for. (In other words, the company that pays me provided neither the computer nor the network.) My "employer" asked me to use a program called Hubstaff to track hours worked. I agreed to use this program, not knowing that it apparently takes random screenshots of my screen as well as tracks all URLs that I visit. I just found out today, by accident, that Hubstaff is tracking and saving all of this information.

I have not visted any objectionable sites while working, or anything like that...I don't ever visit those kinds of sites, even when I'm not working!

However, I did access my bank account online while working. (I needed to do so to order a headset that I need for work). I'm concerned that some of this information was somehow stored. I also use a personal email address for work, as my "employer" did not provide me with one. I don't get much personal email in that particular account, but things do come in from time to time, and I am not comfortable with the idea that my personal email inbox could be subjected to screenshots.

I also often listen to podcasts and YouTube videos (documentaries, etc...) while I work. Again, nothing inappropriate, but I am afraid that I could be accused of not working, even though I simply listen to them as I work.

I am also concerned that I could forget to turn Hubstaff off when I finish working, and have my personal computer activity tracked. I would go in to manually adjust my hours, in that case, but I don't know if Hubstaff would erase the information saved...

Given that the "employer" is not even an employer, since I am an independent contractor, and that they provided neither the computer nor my Internet connection, do they have the right to track all of this information? I am not really comfortable with having my personal computer and email address tracked in this way...

I feel that they could have at least informed me of this, as I could simply have used my iPad to access online banking, as well as my email account. If it were company-supplied equipment or networks, I would expect everything to be monitored, but I didn't expect them to monitor my own computer without even letting me know!

The employer is based in Washington state, and I work from a home office in Italy.

Many Thanks.