If you are using the 'button' content block in the UI and not something custom made, you will need to change the 'mobile styles' section on the template to make sure the button displays your new color. Be aware this will overwrite all button colors upon going to mobile.
First you go to the 'Template' tab in the email Content Builder Screen
Then you need to navigate down this tab until you find 'Mobile Styles'
Then finally you go down until you find the 'button' section. Here you will change the color to what you want the default mobile color to be.
Your other option, if you don't want to make the color change universal, is to go into the HTML for that button and add
!important to the
color:#AAAAAA (where the
#AAAAAA is your hex color code.) css attribute for the button. This will overwrite the media query that would overwrite the button on mobile.