By travel hoop do you mean a collapsible hoop? It probably depends on how big your hoops are. My hoops (opened) are about 32" in diameter and made with 1/2" tubing. When I collapse them they are plenty small enough to fit in a suitcase. If you have larger hoops it may be more difficult.

I carried on a hoop in August. I had it broken down into 3 pieces. When security saw it, they all looked concerned and on of them said in a stern voice, "Is that plastic or metal" I giggled and answered, "plastic, it's a hula hoop" They laughed and let me on. The flight attendants even went out of their way to put it in a safe place for me. I hope this helps.

I have a 42 inch may 44 inch infinity hoop that I took on with me and put in the over head compartment. The security check gave me a funny look b/c they didnt know what it was and it has metal in it, something I found out later. it got scanned and was not a problem. It fits perfectly in the over head spot I put the my Bag on top of it. I am the type of person who was a carry on plus a large purse and the hoops and no one has ever said anything.

I recently flew to California with 4 of my LED hoops in tow, and had a much easier time than I had anticipated.
I coiled the hoops down to half their size (they were 38'' & 33'' diameter to begin with), strapped them together with velcro one-wraps, and put them inside a hanging clothes bag which I folded in half. The security scanner guy gave me a funny look and asked "what are these?", and when I happily said "light-up hula hoops" he just laughed. I was a bit worried because of the wiring and lithium-ion batteries inside them, but it didn't pose a problem at all :)
The hoop bag fit nicely in the overhead compartments on all 4 of my flights.

I flew recently with a Hoopnotica hoop that comes apart into pieces. I stuffed them in the outside pocket of my wheeled carryon bag. They stuck out the top. My husband couldn't believe that I didn't get a single question about it from security or the airlines. Other passengers asked though. "What ARE those?"

I loved having my hoop at the work convention. I took it to the exercise room every evening to hoop - great stress reliever.