How to get around iframes with WordPress?

That would be more of a question for the makers of Wrike, not WordPress, since it depends on whether or not Wrike has APIs or some other way to access their data. A quick glance at their site reveals they do have an API – developers.wrike.com – you would create code that pulls the data from their API, then outputs whatever HTML you want it to, and you could then either place your code in a plugin (if you want this functionality even if you change themes) or within your custom theme (if you include a lot of styling/formatting in your code and it’s tied to the theme).