Pour half of the churned strawberry ice cream base into a freezer-safe container, top with the raspberry puree and swirl the two mixtures together, not stirring too much. Then pour in the other half of the ice cream, top it with the remaining raspberry puree, and swirl again. Place plastic wrap, parchment or wax paper directly on top of the ice cream, cover and freeze for an additional hour (for soft-serve consistency) or a few extra hours (for hard ice cream).
If you aren’t using an ice cream machine, once the ice cream base reaches a soft-serve consistency, pour the raspberry puree over the ice cream and gently swirl the two mixtures together. Return to freezer and periodically stir (beat) the ice cream until completely frozen. It will likely take a few hours (from start to finish) to be ready.