"I'm not a robot"

There's probably little you can do at your end. T-Mobile shares one IP address among many of its customers, so Google interprets all the various users as if they were one person making lots of requests at the same time, in other words, as some sort of bot.  Can T-Mobile work with Google to sort this out? Maybe, but the only thing we can do from our end is to do something that will get us a fixed IP address, like using a T-Mobile business account and paying extra for a fixed IP address. Or we can just keep "proving" we aren't bots by using those annoying "prove you're human" tests.