Need Cleaning Suggestions

[Michael Temple]

I have a house I am rehabbing and someone suggested I glaze over some tiles in the stove cabinet to make the colors match better with the kitchen. The problem is I am pretty sure nobody cleaned these walls in 30 years. They are sticky and have grease/grime on them. No amount of scrubbing seems to get them cleaned. I need to have them really cleaned for the glaze to stick and I REALLY don't want to have to remove and replace them.

Does anybody have any suggestions for some super cleaning chemical that will cut the grease and sticky crap?