It is difficult to say for certain, but from the images you sent, it appears as though the white/green material is bird droppings on the ground under the tree. If this is a place that birds like to roost, then this may what you are seeing under the tree. Another possibility is that it is a slimemold that is common in mulched areas in landscapes called 'dog vomit slime mold'. It grows on mulch and other decomposing items in landscape areas and does not pose a danger to the tree. Here is a link on information on this slimemold: http://mdc.mo.gov/discover-nature/field-guide/dog-vomit-slime-mold-scrambled-egg-slime-mold