Thanks for posting your question and for your support. Sure, we could remove the LinkedIn icon with a little Custom CSS. However, if you’d like to change the design then it might be best to change icon solutions. Here is another way of doing this:
Install the Jetpack plugin if you aren’t using it yet. Connect it to your WordPress.com account and then go to Jetpack > Settings and click the search icon, typing sharing and enable that module. Next, click the down arrow on the right of the module and click the Configure your settings link. Once on the configuration page you can now choose the networks to use and their styling and where to display the links. Please, give this a try and let me know how it goes.
I would also like to deactivate not just the linkedin button but all of the button under the articles. I would prefer not to use Jetpack. Could you please provide the Custom CSS solution outlined above?