What could this be about? [TsLint Error: “Promises must be handled appropriately”]

That’s a crappy error message. A better one might be,

every expression of type Promise must end with a call to .catch or a call to .then with a rejection handler (source).

So, for example, if you do

PromiseFunction()
  .catch(err => handle(err))
  .then(() => console.log('this will succeed'))

then you will still have a tslint problem, because the type of .then(...) is a promise, and it has to end with a catch. The fix would be appending a .catch clause, for example,

PromiseFunction()
  .catch(err => handle(err))
  .then(() => console.log('this will succeed'))
  .catch(() => 'obligatory catch')

or just disabling tslint for that line via:

PromiseFunction()
  .catch(err => handle(err))
  // tslint:disable-next-line:no-unsafe-any
  .then(() => console.log('this will succeed'))

Alternatively, you could reverse the order of the .then and .catch statements. However, that stops the .then from executing if an error does occur, which you presumably want if you encountered this problem.