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You can remove it but you do need to mention the branding on your site. Below is an example.

This site is protected by reCAPTCHA and the Google
   
<a href="https://policies.google.com/privacy">Privacy Policy</a> and
   
<a href="https://policies.google.com/terms">Terms of Service</a> apply.

Note: Use the following code to remove the badge

.grecaptcha-badge { visibility: hidden; }

See more details HERE – Google FAQ