What can I do with this muddy mess?

Ivy will grow in the shade and it's easy to trim. Or you might be able to find a different shade tolerant ground cover.

Hard to grow grass under trees. The shade, tree shedding, and sap dripping. Not to mention the deep root system that robs the soil of nutrients and water. Ground covers or shade loving plants are the only solution.

Have you tried ground cover, many will grow in the shade.

Just say NO to ivy, please! It is highly invasive and will KILL the tree if it gets into the branches.

I agree with Jeanette, about the ivy. Have you seen stepables? Some of them grow well in shady areas and you can walk on them without killing them.

https://www.stepables.com/

The Ivy is very invasive and will choke the life out of your tree.

The idea of stepables is very good, i was thinking about thyme which is one of the stepables with a pleasant fragrance. Very durable and easy to grow.

I'm no expert, but I'm wondering about the quality of the soil? Even though it's under a tree, it appears to get a lot of light, it doesn't look like a dense shade. Your soil may need nutrients, or something...also, I had grubs that ruined almost my entire lawn...Sometimes you need expert help...But if you don't need the space to walk on, I made rock lined gardens under my pine trees. You could add plants that are suited for your area. (But again, you may need to check the soil before planting.)But you could still border it and fill with mulch or something. You could add lawn ornaments and potted plants...

Hi Roberta. That looks like a perfect spot for a nice garden bench or bistro set! The tree is fantastic! Some decorative stone or mulch, along with some large colorful plant pots will make it a great destination in your yard. If you really want grass, you can use outdoor grass carpet cut to size. It's less money than faux turf, lasts many years, and is easy to keep clean with a leaf blower or plastic rake. It still allows the rainwater to penetrate and keeps the weeds away.😊

I totally agree with those who said no ivy. It's too invasive and really hard to get rid of. We've had good results with vinca minor near our trees.

I'm not familiar with the Linden tree root system so I don't know how much soil you have to plant things in but the stepables sounds reasonable as they don't require a deep root system. You could try several of the herbs as ground covers. I use oregano, thyme, mint etc.... Be aware though that some of those can be invasive too. I would also check into native plants for your area. A lot of the time they will do the best as they are already used to your climate and soil type.

I filled the area with sand and then put bricks ina circle pattern around a tree I had in a former home.

Perennial vinca is a good groundcover for shade or sun.

Talk to your local garden center about Heuchera. The Lime Marmalade works in a shady spot, but there are many varieties. I have various heucheras planted under trees in my yard. They spread but have not been invasive and are easy to care for.