In a medium bowl, combine the water and tea leaves. Steep for 5 minutes, then pour the mixture through a fine-mesh sieve lined with cheesecloth and set over a medium bowl (discard the hibiscus solids). Add the sugar, salt and pepper to the hibiscus water and stir to dissolve. Add the lime zest and juice and stir to combine.
In a medium saucepan set over medium-high heat, combine the strawberries with the hibiscus mixture. Bring to a boil, then reduce the heat to medium-low and gently simmer, stirring occasionally, until the strawberries break down and the mixture is thick and jammy, about 1½ hours. Remove the pan from the heat and cool. Transfer to an airtight container or glass jar and refrigerate for up to 1 week.