I sent an email to Zeiss, complaining about the filmy streaks left on my lens by their Zeiss "lens cloth" product (180-packs on Amazon, etc.). To my surprise, it turned out that this product was not intended for lenses.
Here is their response. I "XXXX-ed" out the personal info.
The product you refer to is sold by the Carl Zeiss Vision division and is intended for use on eyeglasses and not multi-coated camera lenses. I have forwarded your message to them for follow-up.
The Carl Zeiss Camera Lens Division has a line of lens cleaning products which can be purchased through any of our authorized dealers. These include a lens cleaning fluid in a pump spray bottle, pre-moistened lens cleaning cloths and microfiber cloths. I have attached a list of these dealers for your reference. Alternatively, you can use any quality lens cleaning products that are designed for camera lenses.