Today when I tried to check voicemail from a landline, I dialled my own number as usual. As soon as the outgoing greeting started to play, I hit *. The voice prompt said "Please enter your password. Thanks for using Koodo voice messaging service. Goodbye." and hung up.
After some trial and error, I found that I have to wait for the greeting to finish playing. If I wait until it says "Please leave your message" I can then hit * to enter the password and it will wait for me to enter it.