I have a mediocre (3.3) GPA in undergrad due to illness (legit - I had to take a medical leave and was hospitalized), but I have great grades from my graduate institution. I worry that search committees will not look highly upon my application. As I would like to apply for these positions, so how should I tell the search committee why I did poorly in undergrad?
Don't mention anything about your undergrad GPA in your application if it is not mandatory. During interview, if they get to know and ask, you can tell every problem you faced during undergraduate career and show up your proof such as medical certificate. They will consider it.
If it is a mandatory option, then write it down. However, in such mandatory situation, be straightforward (as said by @AlexandersWilliam below) and mention about your poor performance in undergrad period somewhere in your CV or resume, but not necessary always. Because selection committee care less about undergrad GPA, they mostly see your recent records. Hope this will work.
3.3 is not so bad, actually, at the undergraduate level.
You have your medical situation as a valid explanation.
For the right sort of tenure track position --an institution with a true commitment to student-centered education-- someone who overcame obstacles as an undergrad, and can connect well with students dealing with all sorts of problems of their own, can be a real asset.
Keep any explanations you give of the not so good grades you received calm, succinct and matter of fact. (Avoid the emotional approach, and avoid giving a laundry list of difficulties faced.)