The British singer, also known by her married name of Lily Rose Cooper, teamed up with the So What star to record the song, which is released this month (Jul13), and Pink showed her appreciation by showing her with gifts.
Allen received a package of presents for her two daughters, Ethel and Marnie, and the gifts included personalised T-shirts and bags emblazoned with the girls' initials.
The Smile hitmaker sent her friend a message on Twitter.com to thank her for the bundle, writing, "Thank you so much for bubba (baby) goodies. It's an absolute pleasure to work with you."
She also posted a picture of the presents on her page.