Live in Washington, but did contract work in California. Do we need to pay California income tax?

Your question is answered here:  https://www.ftb.ca.gov/individuals/faq/ivr/210.shtml

I work for a company in California. I live in a state with no state income tax. The company has mistakenly been deductions California income tax from my check. I received an e-mail that they have corrected the error and will “back out” my taxes from September. What does this mean?

You'll have to ask your employer, to be sure.  But, it probably means they'll add the withholding money to you next pay check and make negative entries on the California income and withholding so that when you get a W-2 in January it will show 0 CA income and tax.