Both are fine. The course creators aren't exactly fans of swój, but it should be accepted. If not, report it when you have a chance.
If a form of "swój" is correct, it's always better. In 1st person I'd say that "swój" and "mój/nasz" are more or less on the same level. 2nd and 3rd - it's important to use "swój".
In 3rd person it actually changes meaning whether you use jego/jej/ich or swój.