Really, sometimes you have to wonder about TV shows and computer technology on them. Some of the stuff they pull makes absolutely no sense.
First off, the concept of tracing an IP address to a real-world address is somewhat iffy, without ISP help. It's conceptually possible, though, assuming the ISP actively tracks which IPs are assigned to which subscribers.
However just getting the IP address isn't going to get you a real-world address. IPs are usually dynamically assigned. In today's world of constant-on Internet connections they're not quite as static as they were in the days of dial-up, when all that was required to get a new IP was to disconnect and dial in again, but they still change.
But I'm willing to suspend disbelief on that point. Tracking an IP address to an individual ISP account is most certainly possible, and tracking it to a physical address through the ISP is also possible. But it would take more time than most TV shows demonstrate.
The next thing, though, is the "encrypted IP address" which is just completely bogus. What's annoying is that they have a real concept which they could use - an anonymous IP address - but they went with "encrypted" instead which is bogus.
Actually, so is "anonymous IP address" unless you assume it's jargon, which is a fair assumption in my book. In that case it just means that the IP address in question is known to run an anonymizer service, which makes it impossible to determine the original IP address. (See: tor.) This isn't at all the same thing as encryption, though. The source and destination IP addresses are always known. If they weren't, it would be like mailing someone a letter with no return address and then wondering why you never got a response. (On that note: Aphelion, if you ever read this, you didn't bother to leave any contact information!)
In order for a response to be received, the final computer has to know the original IP address. So the IP is never encrypted. (Anyone who brings up IPsec should be enough of a nerd to understand the difference.)
In any case, they manage to track the "encrypted IP" as 3098.41.60.5. Which isn't a valid IP, which is fair enough since most phone numbers on TV shows aren't valid either. But unlike 555-0[01]\d\d numbers, this IP isn't even close to valid. An IP address is simply four bytes. A byte has a range of 0 to 255. 3098 is way out side the range of one byte.
I wouldn't mind something like 398.41.60.5, which is also invalid, under the assumption it's just a "555" IP address. But come on. 3098? Not even close.