The risk of your bird chewing on and ingesting strings/threads from either his toys, from towels, from clothing, the carpeting, etc. is very, very great and usually fatal if not caught in-time..But it's not immediate, and as a result people think that it's fine for their birds to chew-on and ingest little tiny bits of material, because the bird has been doing it for a long, long time with no health issues at all...And that's why it's typically deadly after a long period of time of doing it, you don't see it coming at all..
This is one of the two major reasons the "Happy/Snuggle Huts" have killed so many pet birds, it's exactly the same situation. The bird chews on the material, whatever it is (even natural cotton is not fully-digestible by birds) over a long period of time, and they ingest it little by little over the span of months to even years. And then depending on the size of the bird, the accumulation of the little tiny pieces of material form an obstruction somewhere inside of their Gastrointestinal Tract, somewhere between their crop and the distal end of their intestines (the larger the bird, the longer it takes for an obstruction to form)...and then one day, out of nowhere, the bird starts displaying signs of being extremely ill, they start passing blood in their droppings, or stop passing droppings all-together, they start vomiting-up everything that they eat because it cannot pass the obstruction, and by the time you get them to the CAV, they do an x-ray, ultrasound, or CT Scan and find the obstruction, the only thing you can do to save their life is surgery to remove the obstruction. Most birds don't even get that far, they end-up developing a horrible infection from the material sitting inside of them for such a long period of time, or worse, if the obstruction is located inside of the intestines it can cause an actual rupture of their intestines, spilling the waste inside of their intestines into their abdominal cavity and resulting in a usually-fatal, systemic infection called peritonitus, the same thing that most people die from when their appendix ruptures inside of them...
SO, the answer to your question is no, it's not okay to let your bird chew-on any type of fabric such as towels, blankets, or any fabric/rope/string on his bird toys...The best thing you can do is the minute you see any of his toys that contain any type of fabric, rope, twine, string, etc. starting to get threads hanging, throw it away and get them a new one...or simply don't buy them any toys that contain non-digestible fabric, rope, etc. And as far as your bird chewing on the towel you've got on the leather couch on a regular basis, again, not a good idea at all...You're best to either keep him off of the couch all-together, or get some type of vinyl, plastic, etc. cover for him to sit on when he's on the couch (and then give him a toy or other activity to do while he's on the couch so that he won't go after the couch itself), or better yet, as stated above, buy a big mat made out of seagrass and put it down for him on the couch...
