I live in an area where there are no phone lines, but a strong cell signal. I get internet through a tethered connection to my cell phone- it is metered and fairly expensive. So in my listing description I mention that internet is limited- fine for doing email, surfing the web a bit, but no streaming, uploading or downloading large files, or Facebooking, etc. for hours, as those sites automatically play videos, post photos and so on.
All my guests have been fine with this- they almost all go into town daily, where most of the cafes and restaurants have internet connection which their customers can use, if my guests need to be online more.
I'm not off-grid- I am on city water line and electric, but my place is in the countryside, so I get a certain kind of guest that prefers not to be right in the midst of the hustle and bustle of a busy tourist town and doesn't mind the 20 minute walk to town and the beach. Several have said they are glad I don't have unlimited internet, as it is too easy to be online for hours, which they didn't need to travel to a Mexican beach town to do. Most of my guests are readers and enjoy having the time to do that while on holiday, as opposed to being constantly plugged in.