Ask HN: As a remote worker, would you resist screen monitoring software?

I run a small software development company, about 10 remote software developers. I have great relationship with them and they are really good developers. From time to time I have a feeling their productivity is not great. Also they fill their time sheets once a month and I am not sure how accurate their time reports are - which we use for billing.

I don't want to invade their privacy and don't want to send them a message that I don't trust them if I recommend screen monitoring software like Time Doctor. I understand that like inhouse staff they have right to waste some work time too, but my nature is that sometimes I think about it too much and doubt my staff if they really work. This affects my relationship with them and I am trying hard to prevent myself from showing it publicly.

Time tracking would probably solve my uncertainty and make me feel better about their productivity.

I am thinking of giving them a payrise - e.g. 5-10% if they accept the use of this software.

Would you accept this offer if I gave it to you?