The top tether is there to make the seat more safe. That is, "in a car seat restrained only by the lap belt" is not as safe as "in a car seat restrained by both the lap belt and tether." That said, it's still safer than "not in a car seat, just using the seatbelt or held by a parent."
You can buy a seat that doesn't have a top tether, to be sure - but such a seat isn't magically safer than one with an unattached top tether. Generally it will be a rear facing bucket seat for a tiny baby. (In North America, all forward-facing seats manufactured in the 21st century have tethers.) If you have an older child, I would still think an untethered size-appropriate seat, restrained with the lap belt, would be your best choice. If your issue is that you think the airline will reject your seat, look for a sticker that asserts it is approved for use on airplanes, and be prepared to show the sticker to the crew.