To remove a vendor alert (and to discontinue the vendor alert emails), you will need to go to the "My Perks" section of your profile. 

Here you will be able to locate an "Alerts" section which will show the vendors from whom you have selected to receive alerts. Select the vendor from whom you wish to no longer receive alerts. When the page loads, de-select the highlighted blue "bell" shaped icon next to the vendor's profile button.

Once this has been de-selected, the vendor will be removed from your "Alerts" section and you will no longer receive vendor alert emails from that vendor.