Official context first, then the cleaners whose makers name this grime.
Our explanation written by Grimy Hands
HSE lists oils and greases, and solvents, among some of the more common causes of irritant contact dermatitis. The cleaners below are the ones whose makers name grease or oil in a claim about hands or skin; each product page carries that maker's cautions beside the claim.
Our explanation of the official sources quoted below. It adds no facts of its own and doesn't rate or recommend any product.
Official context
These are some of the more common causes of irritant and allergic contact dermatitis:
Big Wipes hand cleansing wipes remove anything from water and oil-based paints to varnishes, silicone sealants, oils, epoxies and stubborn Poly foams and adhesives.
The scrubbers, along with synthetic and plant oil-based solvents, removes stains from hands including motor oil, carbon black, automotive fluids and adhesives.
It is formulated with surfactants, walnut shells and pumice to help exfoliate the skin and remove even the toughest soils – paints, inks, oil and grease.
Lava Soap's pumice cleaning power is used by mechanics , DIYers, professionals, hobbyists , gardeners , and more to quickly break through grease, grime, glue, goop, dirt, tar, oil, sap, paint, and anything that can collect on your hands while working on projects.
This creamy-white, viscous hand cleaner harnesses and enhances the natural cleaning powers of citrus oils to penetrate and remove dirt, grease, grime, ink, tar, carbon, resin, paint, adhesive, oil, and asphalt.
The maker's stated use, not a safety recommendation.
General information, not medical advice. HSE: Skin dryness and cracking are early signs of dermatitis and shouldn't be ignored – you should check with your GP or if available, your occupational health service if you notice these signs. (source)