Excellent answers already; one point no-one has covered is that greys will occasionally eat eggs / chicks of small birds. Wikipedia says there is a lack of evidence on the actual impact of that, but it is something that does have a wider effect and that reds very, very rarely do.
However, there is, in the UK at least, also a reverse viewpoint. The introduced grey squirrels are greater generalists than the reds. Red squirrels thus suffer far more from habitat destruction and climate change than greys.
You often see greys bouncing along the pavements in my town, a city of 250,000 - they can live in parks or gardens and will coexist with humans and eat a wide range of foods; whereas reds are limited to conifer woods.
So another way of looking at it is that humans have depleted the red squirrel population by destruction of their specific habitat requirements, and the greys have filled the gap. The greys get a bad rap as invasive vermin, but we should really be looking at what we did that allowed them to become so dominant.
Britain’s surviving red squirrels feel the pressure (New Scientist)
However, reds do have some natural advantages; they have greater agility, enabling them to avoid pine martens, a major predator.
In neighbouring Ireland, the population of the less nimble greys
crashed when pine martens became more abundant, while the reds were
Pine marten in search of a snack takes a selfie (New Scientist)
In answer to your actual question, in my view there is no straightforward answer. Liam's statement of "any (unnatural/man made) change in an ecosystem should be resisted" is a classic conservation viewpoint, but there are other ones, and once a change such as an introduction of an non-native species has occurred then any attempt to resist risks being an even more dramatic man-made intervention. Also, a species as successful as the greys will spread widely itself - at what point does their population growth into other areas become natural rather than introduced?
And of course, reintroduction attempts such as the UK beaver reintroduction blur the line - a reintroduction is clearly an unnatural change. Should we accept that a snapshot in time when beavers were a native species has gone, and conserve the current moment, or should we try to return to and conserve the past?
Grey squirrels have been in Britain since 1876; when do we start considering them just a highly successful endemic species?
DISCLAIMER: I am not an ecologist; I just have a fascination with ecology and have developed a recent interest in grey/red squirrels in the UK :o)