If I am creating a website to filter retail websites, like shipping or eco-friendly, etc. Could I use the screenshot of the homepage as the icon to link to the direct website? Ie. if my filters result in the The Gap, www.gap.com, and there is a snapshot, cache of the homepage, am I infringing on their ip?
You should contact a lawyer versed in IP law in your area and this is not legal advice.
It looks like this can fall under Fair Use in North America and possibly other regions but be prepared to take down things on request. That is what Google does. Should you think there would be grounds for this to be infringement, someone would most likely sue Google rather than a small site.
Note that Fair Use is not a precise concept and balances a lot on how things are used. Present it in a way that makes it clear this is a thumbnail for the site you are representing.
There is an even better way to do this: Ask. Considering you are already obtaining data from these sites, you may as well ask your contacts for a representative image. It will usually be much nicer than a screenshot bound to fixed-size image which often becomes illegible.