I've actually seen this happen before, but it is pretty rare. Nick's right, there's no real obvious way to fix this without voiding the warranty and potentially causing more damage.
In my case (not involving an Eventide product), I was able to use a pair of very thin, very long needlenose pliars to go into the jack and get enough grip on the broken tip to pull it out (I obviously disconnected the unit from its power suppply). That can be a tricky procedure and you run the risk of damaging the jack and the pedal (possibly shorting the electronics, even with it unplugged).
The only other way is to open the pedal to get to the back of the jack, possibly needing to replace the jack, definitely voiding the warranty, and very likely damaging the pedal.
My best advice is to either send the pedal to Eventide (which will probably cost, since it's not a fault in the pedal) or take it to a qualified tech (which will likely void the warranty). Unless you get really lucky and the broken tip just falls out on its own. I can't recommend trying to fix this yourself, due to the risk of further damage and the loss of the warranty.
You might try contacting Hosa, since this is a problem with one of their products. I'm not a lawyer, but in my brief review of their policies from their website, it doesn't look like that'll do much good. Also, you might try contacting the store from which you purchased the TF, if you bought it from a store. They might be able to help.
In any case, I wish you the best of luck… it's just a rotten situation.