Im sorry to hear about your cat's situation. When a pet eats something they shouldn't, we essentially have 4 options.
1) make it vomit- the vet would have to decide if this is appropriate given your cat's presentation. Risks include aspiration or the object getting stuck in the esophagus which would be a potentially worse issue. Furthermore, cats are tricky to make vomit as they do not respond as predictably as dogs do to apomorphine the most common medication used to induce emesis. A medication that has worked for some cats is called dexmedetomidine but this will also cause sedation and require reversal with a medication called atipamezole or you will have to let the sedation wear off.
2) removal via endoscopy. this requires a place that has an endoscope and someone with experience in foreign body removal so this is usually a specialty clinic or an emergency clinic with an experienced practitioner interested in endoscopy. The risk of this is that the object may not be able to be removed with the scope and surgery would be necessary. It also requires anesthesia.
3) the third option is the most invasive but the only way to guarantee removal before it is a problem. Surgery requires anesthesia and is also more expensive than the other options but the only way to know that all of the object has been removed and will not be a problem in the future. Obviously this carries the risks of surgery and anesthesia.
4) the fourth option is to monitor for the passage of the object or development of an obstruction if it does not pass. This is the least ideal situation as we cannot predict which things will pass and which will not and ribbon can be very damaging to the intestines as it tries to pass through- especially if it gets stuck. Signs that surgery needs to be done include vomiting, loss of appetite and abdominal pain. If you choose this option, I recommend adding fiber to the diet to help decrease GI transit time. Caned pumpkin and metamucil are two ways of doing this.
Have I been able to help address your concerns at this point?
My best recommendation would be removal via endoscopy or surgery at this point as if you wait until an obstruction develops, your cat may not survive surgery or recovery due to the complications of bowel rupture or leakage.