This method will lift debris and marks, disinfect, and deodorize the mattress:
Mix a squirt of dishwashing soap with about a cup of water and mix until bubbly. You could also use a stain remover.
Apply that to the stain with a cloth (dish towel, face cloth) and gently rub in circular motions.
Let this sit for a minute or two. Rinse the cloth and blot the stain.
Spray the stain with white vinegar and let this sit for 5 minutes.
Sprinkle baking soda onto the stain. When the fizzing stops, dab it up with the (rinsed) cloth and vacuum the rest.
Feel free to keep us posted on how these steps work out for you, and don't hesitate to reach out if you have any concerns or questions.