The router does not have the power to collect the data and send it to the router company even if it was programmed to do so.
You should always assume someone is looking at your data for invalid purposes even if it is just to spam you with advertising.
You best option is to always use HTTPS, almost every sites runs that already. Then change the DNS in your PC to 1.1.1.1 and use the chrome browser. This prevents anyone from seeing the site names you are using. This is the last small hole ISP were using to spy on people. The google DNS at 8.8.8.8 and the firefox browser are also suppose to support encrypted DNS but I have not kept up on the status, they both had some early implementation issues.
If you are really concerned...