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I have many years worth of run data on Garmin. I would like to start a fresh attempt to run the entire city, so I don’t want to see any data about runs prior to last week. Is that possible? I know you filter on dates but that doesn’t seem to affect the street count/progress count.
Make a new account on RunKeeper or MapMyFitness.
That way you have total control over you new CityStrides map.
Just make sure you don’t link it to your current CityStrides account.
Yeah, this is exactly what Challenges are for. This post makes me realize I need to add more information about them within the site 
You can create a Challenge with a specific start and optional end date. Only activities within that time are counted.
You can also choose a specific city, to get some more info out of the Challenge page.