There is a gadget for this but is expensive, it's like a fine shaver. I very carefully pick at it with a seam ripper till the stitching is all gone, but be careful, as it's not hard to also cut the fabric. I would look at appliqueing something suitable over the patch later, depending on how it looks once the embroidery is gone, and washed.
This is the Australian company that sells the shaver, you may be able to get it in the USA, it shouldn't be quite as costly.
https://www.echidnasewing.com.au/peg...0volt-cordless