There is no SE (start enrichment) thermal valve on a manual choke carb. All you have is the cable going into a plastic piece that threads into the carburetor main body.
At the end of the cable, inside the plastic "holder" is a little metal "slug" or "bullet", for lack of a better term, that may have parted from the cable. The only way to know is to take the entire assembly off.
Also, the plastic threads are somewhat delicate and can strip out as well as the plastic "holder" can crack.
The choke "assembly" is designed to be taken out as one piece before you can work on it. This usually requires that the carb be removed from the engine in order that there be enough clearance to "unscrew" it from the body.
I would advise you that, if you find that the cable and or housing is damaged, don't just buy the one piece.
Buy the whole choke assembly (two separate parts) and have yourself a trouble free unit to re-install.
Below is a parts page link. The two items that make up the choke are 12 and 20. 12 is actually the cable but they (HONDA) refer to it as the "valve set". Item #20 is the plastic holder but Honda refers to it as the "cable". Go figure!....around $33 plus shipping for both.
I also recommend that you purchase two of item #19 to remount the carb with no air leaks. Another $4
https://www.cvs.com/weeklyad/browse/browse-home.jsp#Browse
Be advised that it takes a bit of CARE and EFFORT to assemble the cable (valve set) to the holder (choke cable) and get it working correctly. ONLY after it is fully assembled and moves properly is it then to be threaded back into the carburetor body. If you do not use a bit of finesse to fit these two together, you can damage the holder piece. You can EASILY crossthread the holder into the body and ruin the threads on the plastic. You have to take extra care not to do this when putting it back on the carb.
In addition, IF the holder piece has been "jiggling" around inside the carb housing because the threads got loose in service, it may have damaged the soft metal threads of the carburetor and a new piece will NEVER screw in and hold tight. In that case, you may want to consider buying a new carb. Item 10...$128. As you can see, it comes with a new "holder" or cable (item #12) but not the "valve set" (item #20). If you need to go that route, do yourself a favor and buy a new valve set. Well worth the 16 bucks.
I have successfully EPOXIED the holders back in when the threads have been damaged but epoxy is brittle and you never know how long it will last. Your budget....your decision.
Good luck.
