Hi Ajay,
Catalyst Converter (aka Cat-Con) is a device that uses a catalyst to convert three harmful compounds(Hydrocarbons, Carbon monoxide and Nitrogen oxides) in car exhaust into harmless compounds(Carbon dioxide, Water, Nitrogen).
Position of Cat-con is closer to the exhaust ports of the engine.
So when we try push starting, there are chances to get the fuel spilling into the cat-con and it may results in damaging the cat-con.
No need to worry too much, probability of getting cat-con damage is very less especially when you push start your car once in a blue moon ;) I had a couple of push start kind of starting(starting the car in a slope without cranking the starter motor; just for fun
![Roll Eyes [roll] [roll]](https://www.theautomotiveindia.com/forums/images/smilies/Roll.gif)
)
If you feel something is wrong or you want to make sure your cat-con is healthy then have a SMOKE TEST. That is the simplest and easiest method to check the condition for your cat-con.
I hope this will help you:)
Regards.,
Kiran.