Cork is nice and easy to care for. 

Simply use a nice soft cloth, dampen with water and use a mild detergent. Gently rub the cork and then allow to naturally air dry. If you find that there is dirt that is very ingrained which sometimes happens with the natural colours, then just repeat the process. 
The cork is of premium quality, so cleaning it will not scratch or tear the cork.

Alternatively, you can use an eco-friendly gentle baby wipe or make up remover works as well.