Set the logic board back down, leaving the spudger underneath to prevent the adhesive from re-sealing.

In the following steps, you'll use a liquid solvent (such as iFixit Adhesive Remover or high-concentration isopropyl alcohol) to weaken the adhesive under the battery. The location of the adhered areas and the Smart Connector flex cable underneath the battery are shown in the last two images:

Adhesive

Smart Connector cable