I have a 'back to top' arrow, which shows when you scroll down the home page. It works based on interactions. Whist it appears to be visible on both tablet and mobile preview modes, it doesn't appear on screen when actually looking at it on a tablet or mobile phone.
Below is a pic of the tablet preview mode - note the blue back to top arrow on bottom right hand side of screen.
Below is a pic of the site on an iPad. Note the lack of blue arrow.
Looking forward to some insight!