I typed in my password in Microsoft password strength checker website. Could it now be possible for someone to recover that password from my computer?
From your computer - Not any more than usual, no.
However the owner of the website you used could very easily have a copy of your password!
You shouldn't ever use an online password checker, as you have no control over where your data has gone.
As Neal stated in this answer on a very similar question:
I assume you're referring to the Password Checker page on Microsoft.com.