If the customer is in a level that gets a discount on a product, that product will show a special label next to the price.
That label is the customer level name plus the regular price label, which is usually the "showproduct.aspx.27" string resource. It sounds like maybe that's been cleared out on your site, so you're just seeing customer level name.
There's no configuration to remove that, but you could use CSS to hide that element. Recent versions have it styled with the 'level-price' class.