Bathroom Sink Has Mold or Mildew In Overflow Drain Hole

I noticed a bad odor coming from *inside* the bathroom sink. I looked inside the overflow drain hole with a flashlight and sure enough, there's mold (or mildew?) growing in there!
Would some dilution of Clorox + water work? And how can I get the Clorox down into that narrow hole? Any type of brush that is narrow & flexible enough to get down into that hole?
Thanx in advance!
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Steven D. Litvintchouk
Email: snipped-for-privacy@earthlinkNOSPAM.net
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Steven D. Litvintchouk wrote:

Chlorix is good, but that "hole" is a concealed passage which goes all the way to the drain (pop-up) opening. Very hard to clean of the soap scum which the mildew lives on.
A turkey baster might work for this.
Jim
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