As an added precaution, I always check my oil filter for slivers of metal, possibly from clutch wear and alike. To do this I stick a white paper towel inside the oil filter so I have the silver metal or any other alien form pops out from the white paper towel background.
After that I use compressed air to blow the filter clean from the inside out. This frees it of all debris.
I emailed my mechanic, who worked for Bajaj USA at their corporate office and at a Bajaj dealer (also Vespa, Lambretta, and everything else) as a head mechanic, and this is what he had to say:
"Be honest with you, I have been a mechanic for almost ten years and I have seen a lot of crazy stuff coming out when performing oil changes. Normally, I will not worry about it unless the engine sounds weird or runs like crazy.
Do you have any problem with the engine? Any oil leak? Any idle issue? If not, then don't worry about it since those pieces are already broken or came off."
With that response, I filled it up with new oil and will ride the bike and pay special attention to it as all of my answers are "no" to my mechanic's questions.
Looks like those things are the engine case paper gasket. Do you have any oil leak out from your engine? If not, don't worry at all.
What happen are..... those engine paper gaskets for most of the time are larger than what it is supposed to be. And sometimes due to the engine design, gasket can't cut out exectly or match the engine cases because if everything matches the paper gasket are not strong enough to seal, hold and keep the oil inside the engine. For some cases, when the extra stick out paper gasket inside the egine has soaked oil for too long, they will be soft enough and tear themselves apart. That is what you see in the screen filter. And that is why engine will leak oil when they get old. And of couse, the material to make the paper gasket is also important. For bajaj you don't expect they are top qualities.
So for now, if you have any oil leak, you know what happen.
Hope this information would help you.