Excellent and informative pictures!
The worry here is that the back of the baseboard is wet and that the curb is stained. You have to ask yourself where the water is coming from. It could well be behind the shower wall and under the curb and the baseboard and the drywall behind it are just the tip of a wet, moldy iceberg. Don't use the shower and get someone in to take off a few tiles if you don't feel confident doing that yourself. My bet is the tiles will come off very easily.
Q