Hello Mitch,
I suppose you mean update to 3.7.7 and not 3.3.7 as the current live version is 3.7.7
And although we have tested this ourselves and did not face the issue, I will double check it for you. In the mean time, you can be on the safe side by following the steps below (provided that you have not edited any core theme files and all your changes are done though the child theme):
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Go to Appearance >> Customize >> Import / Export and the Export your customizer settings and save it locally, it will be saved as a .dat file and you can name it customizer.dat
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Activate the theme.
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If you notice that colors are not your customized colors, go to Appearance >> Customize >> Import / Export and then Import the .dat file you saved in step 1.
Now you should have your colors back, if it was lost in the first place.
Thank you