Exclude term(s) from the Layered Navigation Widget

Hi,
I have been digging in Woocommerce source code for a few days now and can’t figure a “nice” way to add some behavior to the Layered Navigation Widget.

I would like to add an option to the Layered Navigation Widget that could allow me to exclude terms from the widget.
Let’s say we have a “Provider” custom attribute (on products) and that we want to hide the products of a specific provider in the shop page. When this is done thanks to the pre_get_posts hook by modifying the main query, the “empty” provider still appears in the sidebar within the Layered Navigation Widget.

Is there a correct/clean workaround to this ?

https://wordpress.org/plugins/woocommerce/