The Leeds, Grenville and Lanark District Health Unit wants to help clear up the concerns over restaurant customer logs with the following information:
Only contact info (name and phone number) needs to be shared.  No personal health info or other details.
The restaurant keeps this information for 30 days and only shares it with Public Health IF there is contact tracing that needs to be done as a result of a customer or staff member testing positive for COVID-19.
Restaurants already collect this basic information if you make a reservation or order take-out.