Wart on finger was pulled off after using Compound W, what is the white plate like thing that was once under the wart? (photos)

Been applying Compund W to a wart that has been on my finger for over 4 months, the wart then got loose after 1 day of compound w and I pulled it off. There's a white hard circular thing on my finger that I want to get rid of, I don't know what it is. If I leave it on my finger will it eventually go away? Or will the wart grow back from this white thing? I don't want it returning, what are some steps I can now take to get rid of it and ensure the wart won't come back?

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