Help with changing a background!

The subject's hair has a noticeable green cast from surrounding background and ambient lighting.  In this example, I used Select > Subject and refined with Quick Selection + and - buttons and output to a layer mask.  I added another layer below the subject with a solid, neutral brown background and a touch of linear gradient in same direction as light source. But I didn't color correct the hair.  You can read more about that below.

https://www.photoshopessentials.com/photo-editing/photo-filter/

There are several ways to remove the background. Here is one way that should be fairly simple.

1. With the image of your mom open, go to the Layers panel (if it's not open, go to Window > Layers)
2. You'll see a lock on the Background layer. Click it to unlock the layer (and on a Background layer change it to a regular layer)
3. Open the Properties panel (if it isn't open, go to Window > Properties)
4. At the bottom of the Properties panel in the Quick Actions section, click the Remove Background button
5. Go to the Layers panel menu in the upper right and select New Layer
6. Drag the new layer below the other layer and fill it (Edit > Fill and set Contents to Foreground color) with whatever color you want to be the background color. I'd suggest using the eyedropper tool (for the keyboard shortcut, press I) and sample a darker color from her hair. A darker color will recede into the background and one that goes with her hair will make the edges blend a little better.
7. The layer mask that was added automatically in Step 4 does a pretty good job of getting rid of the background, but there may be some of the original greenish background color showing through her hair
8. Make another new layer and drag it above all the other layers. Use the Eyedropper tool to sample a color of her hair near the green part
9. Select the Brush tool (B) and paint over the green part (it doesn't have to be too neat)
10. Right-click on that layer and in the context menu, select Create Clipping Mask
11. With that painted on layer still selected, in the Layers panel where the dropdown menu shows Normal (that's the blending mode), change it to either Hue or Color--whichever you like better