If you look on the HUBB9 chart, TYR is a transition, so filing HUBB9 TYR should've been perfectly fine. The world low doesn't show all of the fixes, there is thousands, probably even millions of fixes in the United States. The world low is only going to show you the ones that are relevant some how, such as being on an airway.
Another tip, on SkyVector when you punch in your origin and destination you will see in the bottom right, just above where you write the route, a link that says "routes". If you click it you will get a drop down with routes that have been filed in the RW. The heart will mean a commonly cleared route, the green leaf means it is the most efficient. If you look up this city pair, HUBB9 TYR is the preferred route (GARL6 TYR is for Jets below 17000 as noted on the chart). I think you know you can look these up on Flightaware as well, and sure enough HUBB9 TYR is what has been filed and cleared by ATC if you want to verify what SkyVector says.
It looks like HANUH is close to CLARE, but HANUH is an RNAV waypoint while CLARE is a fix. I'm guessing they wanted to route you via the RNAV waypoint like other traffic, but that is dependent on you being able to accept an RNAV waypoint. They should've removed CLARE if you accepted HANUH. Also, you can always ask why when you get an amendment and you can always refuse it if you don't want to do it for some reason.
