It's not possible to only import a few cards and not the whole board, but there are two alternatives for you to see only part of the Trello board in Placker.
One of them is to use the Filter & Settings button to select what are the cards that should be visible (for example, only cards in the "To do" list, or cards with a blue label). After applying the filter, you can save it so it is automatically there when you access the Placker view again.
The other is to create a second board and mirror cards to that board. For example, you can mirror all cards that are created or moved to the "To do" list to a second board and open that second board in Placker. This may be better in case someone must not have access to the first board, because with the previous method, that person could simply remove the filter and see every card.