The Duollingo iPhone app seems to not work with the IOS 7 GM (just released).
sorry I don't have any answer but here (in the general discussion section, called Duolingo or General) your post will be quickly lost in the enormous amount of posts so, to have more answers/explanations to your feedback (or in your case to be sure that Duolingo's team will see it), it would have been better to post it in the Troubleshooting Discussion.
When you create a new discussion, there is a drop-down menu on the top, change from the default value "Duolingo" (which corresponds to this general discussion page) for the specific one (Troubleshooting, in your case). But you can change it now, it's not too late : edit your original post then select the Troubleshooting forum.
Or you can maybe report it directly to Duolingo through the "Support" button.