Cooking grease and butter are toughies. Once they take up residence in fabric, they never want to leave. That doesn't necessarily mean your new T is down for the count, though. Grease stains respond to a number of substances that are gentle on most fabrics. The idea here is to break up the grease and hold it suspended in a water solution until it can be dispatched down the drain. That's actually what dishwashing detergent is designed to do, and spot cleaning grease stains with dishwashing liquid is a great first step. We recommended it in suggestion No. 8 for getting out peanut butter because it works a lot better than you'd expect. Apply the detergent with a sponge or cloth and rub. Then rinse. When you're dealing with a thick, sturdy fabric, you can even scrub the spot with a soft brush like an old toothbrush.
If dishwashing liquid doesn't get the spot out completely, try rubbing it with an alcohol solution. Some spot cleaners use alcohol as a base, so they're a good bet; just check the product's ingredient list to make sure alcohol is a key player before buying one. You can also try using hand sanitizer (which is mostly alcohol), or grab some rubbing alcohol from your medicine cabinet.
If the stain still won't come out, there is a DIY treatment you might want to consider: wood soap. Wood cleaning solution designed for kitchen cabinets is good at lifting grease from just about anything, including fabric. You know the drill: Test an inconspicuous portion of the fabric for colorfastness first. Soak the spot in wood cleaner for 10 minutes, and wash the garment as you would normally. It may take a couple of treatments to get rid of the spot completely.