Slightly moldy starter

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Hello all :)

I've been making sourdough's for a while, but I'm an irregular baker - so after a phase of baking I tend to bin my starters, and make a new one whenever the next baking phase strikes! Anyway, I began making a new wheat flour starter 6 days ago; it bubbled after 24 hours, and looked/smelled right after about 4 days. It's been refreshed daily and kept in a sealed tupperware container, unrefrigerated. 

It's now day 6 - the starter looks right and smells right, but there's a few small patches of green mold developing around the rim of the container? This isn't something I've experienced before - is the starter safe to use, or do I need to bin and begin again?