Sign Up Button

You can do that with the language file, most likely of the theme. I am guessing Whoop but not sure without seeing the site:
https://wpgeodirectory.com/docs/translating-themes/

Thanks

Changing default language strings is done the same way as “translating” default language strings.
That is how you change any default text.

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It should be in the /wp-content/themes/GeoDirectory_whoop/languages/en_US.po file, see image.

Add this CSS for the Log In button:

a.whoop-login-btn {
border: 1px solid #B64425;
background: #e34f43;
background-image: -webkit-linear-gradient(#ff4f43 4%, #e34f43 5%, #c84f43 100%);
background-image: linear-gradient(#ff4f43 4%, #e34f43 5%, #c84f43 100%)
}

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You need to look at the Whoop language file, not the Geodirectory framework language file.

It should be in the /wp-content/themes/GeoDirectory_whoop/languages/en_US.po file, see image.

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Did you upload the files to the language folder of the child theme as explained at https://wpgeodirectory.com/docs/translating-themes/ ?

I am guessing that maybe your Whoop is not up to date, make sure you use the latest version.
Did you upload the translated files to /wp-content/themes/whoop_child/languages ?