How to delete Home and Work address from My Places?
Open Google Maps on your phone, press the white rectangular button with three horizontal lines. It's located in the bottom left corner in Google Maps. Choose Settingsand Edit home or work.

Hope this helps you out.

--UPDATE--

You could also try to log in to google.com from a computer and choose google maps from the app-list (a small icon at the top-right corner with 3x3 dots). Next, click the settings-cog-wheel at the bottom-right corner in google maps and choose my places. Finally click on the drop-down next to my home and my work and click delete.