There are two VERY simple ways to bypass it (so simple that I wasn't sure if I should make a guide, but maybe it can help some people). I prefer the first way, but I'm including the second only because it works. Here you go:
1) Saving the page
Go to your chosen user/pet lookup, do the captcha and enter on it. You will see a page like this:
Then press Ctrl+S and save the page somewhere in your computer, and open it. You will see the same page, but now the address bar will show where in your computer the page is (something like this: file:///C:/Users/Xxxxx/Xxxxxx/Neopets%20-%20User%20Lookup.html). Wait until it loads and press Ctrl+U. Now you have access to the entire source code.
2) Inspect Element
I see no reason why you wouldn't use the above method, but since you can use this one as well I will put it here. Using Google Chrome or Mozilla Firefox, enter in the userlookup you want and do the captcha exactly as you did before, but now press F12 while on the page. You will see this:
Now go to the "Elements" tab and there you can check whatever you want, simple like that.
Well, that's it!
I know this guide is bad formatted (and maybe useless) but I hope it may helps at least one person. Let me know if I can improve anything, and sorry if this is a duplicate but couldn't find any guide like that.