Spath (peace lily) blooms like all blooms have a life cycle. So, the blooms may just be in the down hill stage of the blooms cycle. If the bloom started out white and became light green, then the spathe (hood around the spadix) is simply deteriorating. However, some people believe that the spathe (what looks like the bloom) will turn green when the plant has been pollinated.

I am not sure what causes the greening. Light levels, fertilizer and water could all contribute to this problem. Give it a light fertilizer every week from spring to fall. Keep it moderately moist throughout the year; except winter when water can be reduced a little. If the light level it receives is extremely low try a little more light. De-heading may help. Remove any blooms that are spent. Following the bloom stem to the base of the plant and cut it off.

The most important thing is to make sure the foliage is healthy. This will ensure that the plant itself is healthy. Good Luck