It appears that you were required to carry proof of Financial Responsibility (SR-22) Insurance Certificate to reinstate your license after a suspension due to a reckless driving conviction. From the information we found it appears that you are correct in that a person in this situation normally needs to have SR-22 insurance for 3 years.

To find out if your period for carrying the SR-22 for your reckless driving offense is over you should contact the Washington Department of Licensing (DOL) or other state agency that required you to obtain the SR-22. If your time period for holding the SR-22 is up then the DOL or other WA department should be able to tell you what steps to take in order stop carrying this certificate of insurance.