strange egg white matter...

Hi. I am a relatively new backyard chicken owner.

At least one of our hens has lately begun laying eggs with egg WHITES that have tiny white particulate.

By "particulate", I don't mean dusty or hazy, nor like grains of powder.
These are 5-10 tiny bits of white matter which are very thin--like a thread--and 1-3 mm in length. They don't wiggle or have a black dot or eyes on one end. They are uniform white and symmetric.

I thought, "please don't tell me we are eating 'egg white parasites'..."

Background:
the hens are backyard hens in a 1 ac lot, clean fresh water and green grass and a garden to peck around in, a varied, all natural diet, etc. Overall, suffice it to say that from what I've read on this website, a pretty good living environment overall.

The hens look well. I don't see anything that indicates they are ill. They are clucking, exploring, and eating well.

There is a rooster, one, a Buff Orpington.
The hens are:
--another (2) Buff Orpingtons,
--A sliver-laced Wyandotte,
--A Rhode Island Red,
--An Ameraucauna,

We've noted the particulate in the whites a few times in the last week or so, so we haven't yet connected which eggs they are coming from.

Also note: These are not blood spots. Blood spots are what I keep encountering when I search on the web. This is not a yolk finding. Nor is it a singular punctate brown dot in the yolk.

Any ideas?

Thanks!