Place the strawberries in a medium pot set over medium heat. Warm the berries until they release liquid, about 10 minutes. Increase heat to medium-high and bring to a boil. Keep at a boil, stirring often, until the berries break down and the juices start to thicken, about 8 minutes. Use a wooden spoon or potato masher to help break the berries down. Reduce heat to medium-low and stir in the maple syrup or honey and chia seeds. Cook for about 5 minutes more, then remove from heat. Transfer the mixture to a bowl to cool.
Make the bars:
Preheat the oven to 350ºF. Line an 8x8-inch baking dish with parchment paper, leaving an overhang to use when removing the bars from the pan.
In a food processor fitted with the steel blade, combine 1 cup of oats with the baking powder, cinnamon, and salt. Process until the oats are ground into flour. Transfer to a large bowl and stir in the remaining 1 cup of oats, mashed bananas, and maple syrup or honey.
Press about 2/3 of the mixture into the bottom of the lined baking dish. Press it down firmly and evenly. Spread the cooled strawberry mixture over the top of the crust. Crumble the remaining crust mixture over the top, pressing down gently to adhere.
Bake for 30-40 minutes until golden brown on top. Cool completely before cutting into bars. Store the bars in an airtight container in the refrigerator for up to 2 days.