Quick-desalt the saltfish: Rinse, simmer in fresh water 10 minutes, drain, cool, and flake into bite-size pieces.
Warm oil and butter in a wide skillet over medium heat. Soften onion and scallions for 3 to 4 minutes.
Stir in garlic, thyme, and minced hot pepper. Cook until fragrant, about 30 seconds.
Add tomatoes and bell pepper; cook until the tomatoes release juices, about 3 minutes.
Add callaloo and water. Cover and steam until wilted, 3 to 4 minutes, stirring once.
Fold in the flaked saltfish, black pepper, and seasoning. Toss and cook 2 to 3 minutes.
Finish with lime juice. Taste and adjust heat and seasoning. Serve hot.