A few options to consider:

(1) move the app to show at the bottom for mobile.

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(2) use custom padding inside the app to move it downwards.

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(3) try using "fixed" placement instead of "sticky".

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Didn't work?

Try these alternative apps:

https://apps.shopify.com/quick-announcement-bar-always-keep-your-customers-informed

https://apps.shopify.com/yeps-io