So it sounds like the issue is when you visualize the data in ArcGIS Online after publishing the survey. Am I correct in that?
If so, when you add the hosted feature service to the web map you can configure the popups such that the 1,000's separator is removed. That workflow is detailed here (easiest just to do a CTRL + F for "1,000"): Configure pop-ups—ArcGIS Online Help | ArcGIS
However, another workflow you could look into is setting the field to be a text field and then using a constraint to not allow letters. The way I set this up required a bit of creativity. In the constraint column, I used ".>1000000000" (thereby assuming that all phone numbers will be greater than this, 100-000-0000). So entering A999999999 would not work, because it is still not greater than 100-000-0000). Then to avoid confusion, you can just add something to the constraint message column for that field prompting them to enter only numbers.
Hope that helps!