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My family uses eyeglass cloths from the manufacturer: Ic! Berlin, Lindberg. We wash them in the washing machine, then hang them to dry. Yet before the first wipe, it already contains motes/specks, bigger than dust.
If the washing machine isn't the snag, we prefer not to handwash, to save more effort and time.
I couldn't find any good info on IC! website but chances are these are microfiber cloths. They should NOT be washed in the machine or exposed to any detergent. See https://www.cleanipedia.com/gb/laundry/wash-microfiber-cloths-towels
By machine washing them, you may have worn them out. You either hand wash them or just get new ones. Microfiber cleaning cloths are very effective and very inexpensive, partially driven by the demand for cleaning touch screens from tablets and smart phones.
Something likes this, for example (assuming you are in Germany) https://www.amazon.de/dp/B00EZGFQMC/ref=sspa_dk_detail_4?psc=1 (no product recommendation or endorsement intended. When used as intended (no detergent, little or no water) they work great and last multiple years.
If the glasses are heavily soiled, I do a quick wash with warm water and maybe a tad of dish soap. Otherwise, I just wipe the (dry!) glasses with a microfiber cloth. Cleans all your tablets and smart phones too!
You must locate and eliminate the source of the dirt.
Is the dirt in the water supply?
• Hand fill the washer with clean water. If the dirt is not present after the wash, you must ensure clean wash water.
Is the dirt in the washer?
• Check the filters of the washing machine. If the filters are dirty, clean or replace them.
Is the dirt in the air?
• Check the cloth before and after you hang the cloth out to dry. If the cloth is clean when wet, the place where you dry your wash must be clean.
Work step-by-step to isolate when the problem occurs. After you locate the source of the problem, take corrective action. This might be to change the water supply, the treatment of the water supply, change or clean the washer water filtration system, change the method or location for drying, wash the cloth by hand, accept the dirt as unavoidable, discard or replace the cleaning cloth, use disposable materials.
You could spray them with a stain remover like Shout before washing them, but only if the fabric won't get ruined.
