I hear that you are launching the survey from Leads and from Projects.
For Leads there is a Default Survey setting possible in Admin >> Settings >> Sales Management >> Leads. If a default survey is set it will always be selected and the checkbox checked when you access the Survey Tab in a new lead. The only way to have the checkbox unchecked is to remove the default survey in the "hidden" Settings dialog in Admin. You will need to set Communication >> Surveys >> Lead Default to " " (empty).
If you don't want to save a Survey on a Project don't click the Add button. If you do click Add there is no Default Survey for Projects so the Checkbox and the Survey field on a Project will be blank until you select a Survey. As soon as a survey is selected the checkbox will be ckecked automatically. (If you don't want to save a Survey, don't pick one and close the Survey window......)