Well, at least you're not telling me that they're spoil heaps. The crescent-shaped hill has two names, locally. The north-south part is called Sunny Bank and the east-west part is called Halliwell Hill. These are old Ordnance Survey labels. So another way of looking at them is as two, connected, barrows. Sunny Bank is difficult to investigate as it's under scrub woodland but Halliwell Hill may be investigated in total. Find the northeast corner of it, at 'original' ground level, and identify the forecourt. Once you find and recognise that your scepticism will evaporate. The length, width and height all fit E.H.'s Characterisation Criteria. Yes, it is high, but it's never been ploughed.
If you download my sheet you'll find that I suspect a whole cluster of long barrows around there. Most of them can be argued either way, but not Halliwell Hill - that undamaged forecourt makes it. One of the excavation ditches also arguably shows on aerial images taken during summer droughts. But go and find Thurstones, they're by the side of a public bridleway, just ten minutes from Barrow Bridge, and are easy to find.
And, please, consider what you can give to these monuments - which are truly lost. Will you make a representation to the Museum boss? Or to the County Archaeologist who has never - officially - heard of the barrows at Toothills Playing flds. A round barrow in someone's back garden is pretty scarce. The then Museum boss hopped about with excitement when he saw it - but told nobody about it. Are you just going to leave it? If you've recognised a Round Barrow it's your 'public duty' to notify the statutory body, surely?