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See Eileen's snipping tip: How to give yourself some help with cutting small pieces out of appliqued fonts. And remember to use a fusible applique assist product like Fuse Me on your little applique. It keeps them from shifting.
Pre-cut a small slit into your fabric in the area that you'll need to trim away. Then go ahead with the appliuqe, and you'll be able to correctly position your scissors when it comes time to trim the small area out.