To resolve this issue, edit the card from shared to private. By doing this, it will no longer appear in your co-parent's Info Library.
1) Sign into your account through the TalkingParents mobile app
2) Navigate to the info library
3) Select the card you would like to make private
4) Select Edit.
5) If the card is shared the toggle will be green
6) If the toggle is gray it is private
However, once a card is shared with your co-parent, the information within that card, at the time, will be permanently a part of your co-parent's Info Library Record.