Have you been formally diagnosed with leaky gut or are you self diagnosing? What do you mean by “on week three”, does that include the detailed food and symptoms diary?
Atopic eczema is often multi factorial: genetics, diet (sensitivities/ deficiencies/ gut conditions), overall lifestyle (is it inflammatory), other allergies (dust/ hayfever), how you care for your skin (products/ water exposure). These interact to weaken or strengthen the skin barrier, and to increase or decrease systemic inflammation.
The remove and repair phase of the CG Diet is restrictive to identify food intolerances/ sensitivities, the reintroduction and maintenance phases emphasise balance and a really wide variety of foods. If, say, you had not been eating enough oily fish, it may take some time to restore your levels of vitamin D and long chain omega-3s.
Be aware that overwetting or soaking the skin weakens the barrier and flushes out natural moisturising factors. Also that even residues briefly contacting the skin can worsen or trigger eczema. For me shampoo bubbles running down my arm caused my large elbow patch.
variety.