How about putting a piece of timber across to make a frame? Could support flowering baskets or solar lanterns?

I would get a couple of boards like are at the top of this trellis to finish it off. You could add the grid portion, too, if you wanted to spend the $, but just the toppers would make it look intentional. You could plant some flowering vines to climb the posts. Even annual climbers like Scarlet runner beans look beautiful, cost very little for seeds and you even get green beans!

Ready made trellis panels are not that expensive if the distance between the posts is a standard size. If it isn't you could do a heavy duty rope swag.

Cut them off and plant a groundcover that will grow several inches tall. It's a small garden bed; no one should be walking in it anyhow.

How about stringing or wrapping solar string lights to create a festive atmosphere?

The look below is modern and not difficult (might entail a middle support but that’s not hard to do or expensive). It would really add to the patio.

If you don‘t want to deal with a project, cut down to the base and being located in the garden won’t be a tripping hazard. Add planters if need be on top (and suggest trimming the bushes so they feel fuller/more unified).

Put the trellis back I do not see the issue.

Cut the post and then water around the base that’s left. This will loosen the ground around the cement and you can pull it out. Or you can do any one of the great ideas you’ve received. Good luck!

Now I'm confused. I assumed you were the landlord and were renting this property out. But other posters assume you are the tenant. Which is it?

I too read it that OP is the owner.

Move the plants, and put up a hammock with an awning over it. Or perhaps replace the trellis.

I had several redwood posts similar to what you are showing set in a row of boxwoods and I hung bird feeders from them. Although the dropped seeds can make a mess if you don’t stay on top of cleanup. Just a thought.

Wow, these are all great ideas - thank you! I am the landlord and we are renting this property out to tenants. I don't live near the property so I am trying to get some ideas that I can easily explain to my property manager and the gardener.

That looks great and intentional. Nice that it doesn't block the view out into the yard beyond. It would be pretty with a couple of hanging baskets, too.

Do they have footings, or was the cement poured in to secure the posts?

If the latter, there are ways to remove them. A wood fence builder might be able to do it. Here is the technique:

https://youtu.be/ZkZSvBW0DtE

Update: Just saw your recent posts. This video may be helpful to others.