Equivalent to componentDidUpdate using React hooks

In short, you want to reset your timer when the reference of the array changes, right ? If so, you will need to use some diffing mechanism, a pure hooks based solution would take advantage of the second parameter of useEffect, like so:

function RefresherTimer(props) {
  const [startedAt, setStartedAt] = useState(new Date());
  const [timeRemaining, setTimeRemaining] = useState(getTimeRemaining(startedAt, props.delay));

  //reset part, lets just set startedAt to now
  useEffect(() => setStartedAt(new Date()),
    //important part
    [props.listOfObjects] // <= means: run this effect only if any variable
    // in that array is different from the last run

  useEffect(() => {
    // everything with intervals, and the render

More information about this behaviour here https://reactjs.org/docs/hooks-effect.html#tip-optimizing-performance-by-skipping-effects

The useRef creates an "instance variable" in functional component. It acts as a flag to indicate whether it is in mount or update phase without updating state.

const mounted = useRef();
useEffect(() => {
  if (!mounted.current) {
    // do componentDidMount logic
    mounted.current = true;
  } else {
    // do componentDidUpdate logic