So sorry to hear that your mom is having so many problems. Everyone is different in what they can handle with GERD and gastritis. I don't think weak decafeinated tea would cause her any trouble. Water should not be iced, as that might cause spasms in her esophagus if it's irritated.
Be sure that everything she eats is smooth for a while. The stomach is irritated (probably the esophagus, too), and things that are rough will irritate them further. I was able to tolerate one thing above all others...egg custard. It's also full of nutrition. I would always make it and keep it on hand.
The phlegm is probably the esophagus creating mucous to protect it in reaction to the irritation.
Or...could the reflux be irritating her sinuses and she is getting a lot of postnasal drip that settles low in her esophagus. When I have sinus issues that's what happens to me.
Again, sorry that your mom is suffering.