Thin "membrane" is created if I leave cup of tea for hour or more. And it usually sticks to the inner sides of the cup. But I noticed that when I drink tea with jam or syrup then the cup always clean inside as if the syrup contains some kind of acid that remove that tea-thingy.
The parallel process to deposition of limescale ( that is inhibited by acidic jam) is deposition of products of oxidation of epigallocatechine gallate(EGCG) and similar compounds, that are getting adsorbed on limescale particles and cup walls.
Epigallocatechin gallate (EGCG), also known as epigallocatechin-3-gallate, is the ester of epigallocatechin and gallic acid, and is a type of catechin.
It is found in high content in the dried leaves of green tea (7380 mg per 100 g), white tea(4245 mg per 100 g), and in smaller quantities, black tea (936 mg per 100 g).During black tea production, the catechins are mostly converted to theaflavins and thearubigins via polyphenol oxidases.
EGCG is a polyphenol, vulnerable to oxidation on neutral/alkalic environment, forming insoluble product of intense brown color.
Acidic environment, caused by addition of jam or lemon juice, stabilizes the compound.
Minor natural content of ascorbic acid in fruit juice is protected by abundance of organic acids by similar way.
"The scum on the top of the tea is due to hard water (ie calcium carbonate) deposits combining with the tea and reacting with oxygen."
To dissolve that layer we need to rise acid level: add lemon, jam, syrup or even make stronger tea.