Saffron and coloration - is there a way to know why it gave the wrong color?
So, my question is, is there any reasonable guess as to why the threads gave off a pink color? 


Yes. It's fake. I've had family bring over the exact same thing from Turkey a few years ago: entire bags of "saffron threads" that turned everything they touched pink. It's a known fake product in the Middle East region. The fact that you bought it in an ethnic store is worrying though: I'd expect to find unlabelled safflower there but not dyed threads.


  I want to know what I can do with what I've got left in the box


Throw it out. Even ignoring the possibility you raise that the dye used to create it isn't food-safe, fake saffron isn't useful for anything. In your case, I'd take it back to the shop and demand a refund.



Fake versus Real

Here are some general tips to follow when you're buying saffron:


only the threads matter: the yellow stamens are useless and only add bulk, which is a sign that something's wrong
the scent can't be faked and is unmistakable provided you've smelled real saffron before, however most people are fooled by vendors mixing in threads of the real stuff (adulteration)
it has a characteristic taste (that's highly individual), but will never be sweet
it's a deep yellow to orange hue: saffron should never create a pink colour, though the threads themselves are such a deep orange colour that they can appear red
said colour will appear in liquids but will not fade from the threads, putting a strand on a wet paper towel is an effective colour test
the threads will not dissolve but can (and should) be crushed into powder, they also have a distinct texture and feel
it's hideously expensive: even if you personally know a producer/trader or buy in bulk (i.e. tens of thousands of strands), the wholesale price is still incredibly high (more on this below)


Note that the checks mentioned can all be invalidated in different ways and most simply by the seller pulling a bait-and-switch. As a rule, don't buy saffron as a tourist unless you've done your homework on the seller and product.

A quick note on price. Saffron is famous for being more expensive than gold per weight (in retail quantities) and the reason for that is its incredibly costly production process. More than a hundred crocus flowers go into producing a measly gram and the threads need to be harvested by hand. This coupled with the consistent and high demand means that there is simply no incentive for anyone to sell below market value and that's especially true for retail quantities. The retail markup is significant though, especially given the high base price, and avoiding some of it by buying online or at specialty stores can indeed save you a lot, but your average cook or chef is never going to be buying this for 50% off.



Saffron versus Safflower

Safflower is often sold as "Turkish saffron" and some claim it's a substitute but that's just not the case. While safflower does add colour, turmeric does a better job of colouring food yellow without requiring you to filter out chewy threads later. Safflower adds no noticeable taste to food. Saffron simply cannot be substituted, largely because of the complexity of its aroma (which includes over a hundred compounds). There is no artificial or synthetic saffron for the same reason.