From reading the treaty I think that is the overarching treaty and it makes no reference specifically to BATUS. As I said from what I remember (it's 10 years ago) I thought BATUS had it's own specific terms and conditions to coin an industry phraseBATUS is on a use agreement, not a lease. Originally it was leased, but in 2006 it was converted to an agreement whereby the UK can use the base indefinitely. The UK pay for their operating costs.
Canadian copy of the treaty:
Agreement Between the Government of Canada and the Government of the United Kingdom of Great Britain and Northern Ireland on British Armed Forces' Training in Canada
UK copy of the treaty:
Agreement between the Government of the United Kingdom of Great Britain and Northern Ireland and the Government of Canada on British Armed Forces’ Training in Canada
This UKDJ article explains the history if you are interested.
Britain in Canada – The British Army Training Unit Suffield (BATUS)
UK involvement at Suffield Alberta started in WWII as replacement for UK chemical warfare testing after the UK got kicked out of bases in French Algeria when France fell. Post WWII Canada kept the area as a base, but just what went on there is vague other than it was used for "experimental" work. When the UK got kicked out of Libya by Gaddafi in 1969 they needed a new training area in a hurry (this seems to be a recurring theme here) and ended up back in Alberta under a 10 year lease agreement.
The lease was rolled over several times until in 2006 it was decided to instead convert it to a treaty allowing the UK to use Canadian bases indefinitely. You will notice the treaty is not limited to BATUS, just "use land, air space and installations, and station personnel and equipment, at such sites as may be agreed by the Secretary of State for Defence of the United Kingdom and the Minister of National Defence of Canada".
The UK pays the cost of operating the base, including buildings, civilian employees, utilities, etc. They also use Canadian DND purchasing channels for local procurement of goods and services, for which they pay an administration fee.
From what has been said, the UK will continue to use BATUS, just not use it for armoured warfare training. The stated reasons for pulling tanks out sound quite reasonable, that with far fewer tanks in future the UK can't afford to dedicate significant numbers of them to training in a place which is far from any potential action.