As far as I am concerned, provided the area in question is actually your land, that is conveyed with the property, then Persimmon are not allowed to do anything or enter onto your property without your express permission.
If they were stupid enough to remove your tree that would be criminal damage and theft.
Please take photographs of your garden as it is now and ask a neighbour to witness you doing so.
If they then do anything take more photos if you see them and take legal action!
It could be that Persimmon are trying to meet conditions attached to the planning approval and submitting a Landscaping plan and planting in accordance with it may be such a condition. It may be that trees could not be planted until the correct planting season.
Notwithstanding this, there is nothing to stop you tearing down the tree and anything else you don't like as soon as it is done.
As you say, Persimmon would be better concerned with doing works you want like fixing the defects in your home.
You could also consider yourself fortunate that you actually have a front garden!
Most new homes just have a 300mm wide narrow strip of planting behind a public footpath!