By using the CSS transform property you can achieve changing the width by changing the entire scale of the reCAPTCHA.
By adding in just two inline styles, you can make the reCAPTCHA fit nicely on your mobile device:
<div class="g-recaptcha"
data-theme="light"
data-sitekey="XXXXXXXXXXXXX"
style="transform:scale(0.77);-webkit-transform:scale(0.77);transform-origin:0 0;-webkit-transform-origin:0 0;">
</div>
More details can be found on my site: https://www.geekgoddess.com/how-to-resize-the-google-nocaptcha-recaptcha/