Tucked at the bottom, the cowrie-shell radical 贝 marks words about money and value. A counterfeit is about faking something valuable, which is why 赝 carries 贝.
The outer-and-upper 雁 (wild goose) supplies the exact sound yàn and wraps around the top and left. Its 'goose' meaning plays no part — it is purely the phonetic of 赝.