It's hard to see on an iPhone, but you should be able to see how far the wire was pushed in by carefully examining the red sheath - which should be slightly indented/compressed. Mark that with a pen. Then just push the wire back to that point. That's the easy part. (Marking with a pen is probably over kill - you'll know when it's all the way in).
The "hard" part can be getting it to stay when the bird gets jostled around. So for that you securely tape the wire to the other wires next to it so that it won't jiggle out. If you have duct tape it's best - blow dry to heat the tape so when it cools it will set and last a long time. Electricians tape is good too of course. But even scotch tape will work temporarily. That should hold the wire in place until you get home. If you have access to a glue gun use that instead.
Tweezers could be handy if you've got them.
