Exclude Posts by ID in List of Posts WordPress Dashboard

So, what I am trying to do is filter the list of posts (mine is actually a custom post type) in the WordPress Dashboard by ID.

I am checking another area (custom widget) to see if the user can edit a given post (not, I am intentionally dodging the WordPress roles, etc), if they cannot I want to filter/exclude that post from the list.

I want to take this list:

See Image: https://lh6.googleusercontent.com/-nQLDUpoHUig/T84sUXwqNDI/AAAAAAAAB1o/fzZvCkSjawI/w678-h533-k/list_of_posts.PNG

…and filter out post ID’s that another function returns

Note, you can also answer on Stack Overflow: https://stackoverflow.com/questions/10889077/how-to-filter-exclude-posts-by-id-in-list-of-posts-in-wordpress-dashboard-ad#comment14195659_10889077