The curvy staircase does not give me any Mid-century vibes.

If you mean late 60's vibe, yes, those spindles can give that vibe. But a straight spindle or something more geometric would also fill the 60's back to 40's range. The stairs themselves look a lot more modern than that though, so it might be a challenge trying to pull it back a few decades depending on what the rest of the area looks like.

I don't see any need to change it. It does seem a bit mid century to me.

I rather like it

It’s mid century not mcm (which is fine). Would need to see the rest of the house to make any suggestion.

Mid century modern to me are clean lines and simple

Not all midcentury is modern. There's a lot of other style going on in those decades.

There was lots of 1960s Regency mixed with Modernism in the 50s and 60s. Very few production houses were pure examples of MCM with no other elements thrown in. People didn't embrace Modernism fully. The IM Pei houses here had sweeping curved staircases as an option and some of the bathrooms had French Provincial vanities and fussy lighting. In part because they were production houses and he didn't specify every cabinet or fixture. But I don't think anyone could argue that Pei was other than a modernist architect at that time .

If your house originally skews Modern and this is an original detail, then it's authentic to your house. If your house is not modern and you are trying to make it moreso then maybe cut them off. But it's difficult to convert a house from one style to another. If you like modern furnishings there's nothing wrong with more contemporary furnishings in a more traditional house.

I liked gustaviatex's comment, but I have to double down and say again that the curved staircase is not saying MCM. Is this house perhaps Mediterranean? If you change one element it might end up looking out of place and you will have not accomplished what you're hoping for. We need more context in order to give good advice. What style is this house exactly? Can you show the stairs from the foyer, and even a picture of the front exterior would be illuminating. While you have more latitude in furnishings as palimpsest said, stairs are permanent features and it is usually not a good idea to style them differently than the overall style of the house.

I agree that both the stairs and the detail on the rail give a Spanish Revival feel

Here are a couple of the staircases in the IM Pei houses with a metal rail without the detail:

You can see that other details, like open and closed stringers, were also different from house to house.

But is the OP going for modern? They didn't say. Pastel bathrooms and kitchens and Playboy luxe mansions are also midcentury. The OP could go for white railings and pastel florals or stripes with light fuzzy runners, or gold on the railings with decadent saturated color wallpapers and shag carpet. Or do it up in a more modern style. Or the OP could have a whole nother notion of what the midcentury vibe is to them.

Its definitely cool and interesting and I would keep it.

Here are some examples from that era. The curve is not MCM.

Spanish style was very popular in the1960s. It was midcentury but not midcentury modern.

Not a fan first off but especially not inside-scrolly iron.

I assume you MCM and no those do not work with that style.

I really appreciate everyone’s thoughtful response. We are going to move forward with removing them. The house was built in 1979 and is what I would describe as a transitional colonial, whereas it has colonial elements, but also some more modern elements from the time.

A house built in 1979 is really not authentically mid-century if we're splitting hairs here. And just keep in mind that nostalgia for late 70's/80's architecture may not run rampant on the current Houzz forums, but it will definitely have its day (relatively soon, I imagine). That said, it's your house - if you hate the railing, do what you need to do.