Assalaamu alaykum. I have a website for promoting air treatment products and vacuum cleaner supplies. When visitors click on a product link, they are redirected to the merchant's website where people can buy the product. The products' pictures and descriptions on my website do not include haram content. I found that on the merchant's website, they added some videos in the detailed description of some products in which a woman who is not dressed as a Muslim woman appears; the video may also contain music. My question is: is it permissible to promote that merchant's products? An example from the merchant's website: http://www.sylvane.com/honeywell-hpa300-true-hepa-whole-room-air-purifier.html
May Allaah reward you.

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.

We have previously mentioned the concession to deal with such websites that feature photos, music, or the like in a number of our fatwas because these violations are not intended in themselves on these websites. What is not pardoned in a primary matter may be pardoned in a subordinate matter. In other words, a matter that is not allowed in itself may become allowed if it is only auxiliary to a permissible matter.

As-Suyooti wrote, "An implied violation is excused, but an intended one is not." [Al-Ashbaah wa An-Nathaa'ir]

Moreover, the existence of such violations has become widespread beyond control, so it is hard to avoid them. Verily, the stricter a matter becomes, the more flexible it is dealt with (i.e. whenever Muslims experience severe difficulty in applying religious commands, the Sharia relieves such difficulty).

Ibn Abi Hurayrah was reported in As-Suyooti's Al-Ashbaah wa An-Nathaa'ir to have said, "One of the maxims in Usool Al-Fiqh is that when a matter tightens, it relaxes, and vice versa."

Hence, there is apparently no harm in promoting the products of a commercial website that promotes some of its products in the manner mentioned in the question.

Allah knows best.