Peridot is not normally treated. There is also no commercial synthetic for Peridot. It is a lovely stone but it is a little soft (hardness about 6.5) and brittle. It is susceptible to certain chemicals (acids) & thermal shock so it needs a bit of care, especially if it is set as a ring.
I need to see your stone to be sure, but here are some questions that might lead you to solve this mystery:
First off, are you certain this stone is a Peridot? Most jewellers are not gemologists and may not be able to correctly identify a stone. If proper gemological tests have not been conducted on this stone, it could turn out to be anything!
If you are certain it is a Peridot:
Do you wear your ring often? Do you use creams or sprays? Do you cook or clean with it on? Observe the surface of your stone. Is the polish dull? Are the facets abraded? These cut factors can affect the quality of color of your stone and may cause a stone to look "cloudy".
Hope this helps!
Am a Gemologist