To simplify, you've a got a pipe draining into the yard at grade, and water is pooling at the drain site. The problem is that the grade does not allow for the water to escape. Regrade so that water can drain away. As long as the water does not run out of the drain at high speed, you don't need line its path with a gravel mulch. Since the picture is close up, it doesn't indicate if the fix will be complicated on account of other factors we can't see.

Could you post pictures of the bio-retention planter which would show/explain the general set-up of this system. Bio-retention projects are usually associated with rain gardens. Your picture shows a stucco wall. Where is it located and how does it fit into your planter system? Your project is of a type not familiar to me. But, I often have worked with the bio-retention/rain garden concept.