I mean there's absolutely no denying that TMNT has "Storge" or familial love, baked into its DNA, but I would also argue that the other form of love most prevalent in its various iterations is "Agape," or unconditional love.

Regardless of the story being told, his origins, and the way he is characterized, Splinter takes one look at the turtles after the five of them undergo their mutation and automatically decides that he is going to take care of them, no ifs, ands, or buts about it.