If your mobile device has a Web browser, access your Toodledo tasks at www.toodledo.com/slim. This requires an active cellular data connection.
You can do TRO without a syncing smartphone, no problem. If you ever work away from your desk, print out your Do Today list, make notes on it, and process the changes each day. Some people love this, and Toodledo prints a nice booklet that might be helpful. Instructions are found here: www.toodledo.com/tools/booklet.php
You can also use your mobile calendar to see a mobile Do Today list away from the office.