If you use the standard dockerfile provided in the phpList repository then yes you need to share your modifications back to the community. If you write your own dockerfile from scratch then you don’t.
You can remove the powered by image by enabling this in your config file: define('EMAILTEXTCREDITS', 1);. It will be replaced with text instead. Those links support this community via phpList Ltd., the company which supports the product.
If you make another modifications to the phpList source code then you need to share your changes back to the community, under the terms of the AGPL 3 license.