أَخْلُقُ لَهُ دِيبَاجَتِي
I might wear away the fine surface of my face before him through pleading.
Ukhliqu conveys wearing something thin. Dībājah evokes a fine, smooth surface and here poetically refers to the face.
The intended idea is not physical damage. Repeated requests may cost the narrator his ease and dignity; the metaphor makes that discomfort concrete.