I just put the lid back on and let it warp.
I did notice that the sticker inside a D H Harris lid listing their other scents got all mildewed. I removed it and carried on in my typical cavalier fashion.
Since the bowl is wooden, I'd be more worried about it than the soap. Make sure that the bowl is wiped dry before you put it out to air. I would also leave the lid off the bowl until the soap has dried--perhaps 24 hours.