How do I remove these reflections on the floor from my photos

You say you want to “remove the reflections”, but do you mean the shine on the floor surface, or do yoiu mean the sunlit patches?

I would not try to remove the shine. It’s what defines the floor surface, and removing it would make the scene look dead and synthetic.

As for the sunny patches, I’d just paint on a new layer in Color blend mode. Keep in mind that the color should be slightly warmer in the sun than the shade, so just picking up the surrounding color will again look a bit dead. Pick a warmer color (but don’t overdo it. It’s subtle).

You could try frequency separation. The principle is to separate the fine detail and the low detail (e.g. colours) onto separate layers. That way you can retouch the broad areas of colour without affecting the fine detail.
 

1. Make 2 duplicates of your image layer
   
   Name the lower - "Low frequency"
   
   Name the Higher - "High Frequency"
   
   2. Select the Low frequency layer and use Filter Gaussian Blur (around 6.0)
   
   3. Select the High frequency layer
   Go to menu Image > Apply Image
   Set the source layer to Low Frequency
   Set the blending mode to Subtract
   Set Scale to 2 *
   Set offset to 128 *
   Click OK
   
   4. Change the blending mode of the high frequency layer to Linear Light
   
   5. Now you can clone out blemishes on the high frequency layer and lighten or darken areas, such as those reflections, on the low frequency layer or a layer between the two.
   
   
   
   
   
   * Note - the above steps are for 8 bit/channel images. For 16 bit/channel step 3 changes slightly
   
   3. Select the High frequency layer
   Go to menu Image > Apply Image
   Set the source layer to Low Frequency
   Check "Invert" next to channel
   
   Set the blending mode to Add
    

Dave

As I understand it, you do not want to remove the reflections. You want to make the colors in the reflections match the surrounding floor. Am I understanding correctly?

You could select the highlight and use Hue/Saturation.

.

Not sure I understand correctly, but maybe a Layer with the Blend Mode »Color« can be useful.