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Cleaning the corners of a non stick tawa cannot be done with a steel or scotch bite scrubber except with plastic scrubber. The reason for it becoming black is use of oil while making dosa.
Avoid pouring oil, if at all it is poured otherwise pour on the dosa so that your edges do not become black.
Next is while making dosa have the flame in medium or sim and never on high. For the dosa not getting dark, always cover it and it will not only come out in shape but also won't become black or burnt.
Never pour water while the tawa or any non stick utensil is hot.
You can scrub by using the steel wool but the teflon coating would go. It will become useless.
Use this tawa for making rotis and get a new one and follow the instructions.