How to check if EarPods are fake or not?
Apple has a page to assist in verifying authenticity for some of their products.

For EarPods, there's no easy way to check.  

A few years ago, someone on LinkedIn wrote a nice article with pictures to help people identify real products vs fake. 

It comes down to quality of materials and workmanship.  If you look at the pictures and explanations in that link, you can easily see the type of quality Apple puts into the design and manufacture of their products. Use this only as a guide for things to look for.  They're not the only ways to spot a fake but it's a good start. 

For example:


  Check the bass holes in the EarPod (Clearest Way)
  
  The OEM EarPods will conduct an airflow to the bass holes at the
  bottom of it which be designed for better bass sound. If you cover
  these holes with your fingers, less bass music can be heard.
  
  For fake ones, the “bass holes” are just for “decorating” purposes.
  


As mentioned in the comments, the best way to ensure you have a genuine product is to buy directly from Apple or a licensed reseller.