If you directly uninstall the app from the Shopify admin then the badges & highlights will continue to display on your store.
To completely remove the badges & highlights and delete the app code from your store follow the steps below before uninstalling the app:
1. Click the switch OFF button on the badges home page.
Similarly, switch OFF on the Highlights page as well.
2. (Optional) Remove the 1-line integration code from your theme which you added while setting up the app. The integration guides for badges and highlights are available here and here respectively. Keeping the code will not have any negative impact on your store.
3. (Optional) Delete the snippets/smartb.liquid file and snippets/smarth.liquid file from your Shopify Theme Editor. Do not delete these files if you have not removed the code mentioned in the step2.
4. Uninstall the app from Shopify admin by clicking the Delete button.