The trick is allow the materials to do the work, not necessarily a drain pipe. Although u could get 3” perforated drain pipe too.

I would dig it all out 4” below the drain pipe and gravel, perforate the side of the box drain, then lay the clean concrete sand for those 4” including and envelope around the drain box. Then top the area that had the drain pipe with whatever you want, that is permeable, ie the gravel cleaned out. The sand will carry the water. This is all assuming the drain box goes somewhere with positive drainage.it wouldn’t hit to put sand below the box too, and poke holes in the bottom so there is no standing water.

The good news is their drain pipe worked, the bad news is it got filled with very fine sediment that a proper filter would prevent from clogging.

When you are in clay soils, it is best to use astm c33 sand (concrete sand) instead of gravel. You would simply redig the trench and replace the pipe and gravel, no need for geotextile. The same system is used in dams. Their solution wasn’t too bad, you could probably fix it by digging a narrow trench between the gravel and grass and filling with the sand I just mentioned.

You pictures and description aren’t clear as to what the problem is. Does the pipe not drain anymore? Can you not clean the pipe out? Which way does this drain? It sounds like you have an issue with an outlet that freely drains. Make sure the land is clearly draining away from the outlet. The drainage sock thing others mentioned is for amateurs, not engineers. A graded filter around the perforated pipe is what you need.

Patriots