Can we use difference-in-differences with a biased A/B test?
Why are you hesitant to start over? A/B testing is double-edged sword because it is a relatively straightforward exercise (as these things go) but it has the power to completely pivot your business in a very short amount of time. Plus keep in mind that the thresholds you are seeking to surpass can be "tempermental" (for the lack of a better word) where a z-value of (for example) 1.92 can't be, "oh, that's close enough . . . ". 

As a data scientist, I would never want to sign my name to an experiment that I didn't have complete confidence in both the design and execution. If there is anything that can affect your final scores, you should absolutely consider scrapping it and starting over.