Well, I suppose that access to an internet site is not a material possession -- and so it's not like a pillow.
And I don't know details of the situation you're asking about, but removing a user from a site (preventing their posting there) may be analogous to the Kesi Sutta: To Kesi the Horsetrainer (An 4.111)?
Also I wouldn't describe removing a user as ...
Lord Buddha taught us that "Chethanahang Bhikkawe Kammang Wadami" - Your intentions becomes karma.
In that light, if your intention is to help the patients you are doing a good deed. However, at a much more fine grained level, you have to keep watch of your thoughts. As an example, when you are dissecting an animal or injecting them with some drug ...
For me, the discourse on happiness is a good sutra about right livelihood:
“Not to be associated with the foolish ones,
To live in the company of wise people,
Honouring those who are worth honouring
This is the greatest happiness.”
“To have a chance to learn and grow,
To be skilful in your profession and craft,
Practicing the precepts and loving speech
The associated karma is extremely complicated...
If you are supporting the technical systems, probably OK as your decisions will unlikely have the intent to kill or harm the animals.
If you work in business developments, and have to make a business decision that involves more suffering of animals, there will be Karma associated with it.
Not sure if your work ...