Any authorised service agent will end up sending it back to LVMH in Manchester who change the battery, service and pressure test it. Costs a fortune, takes a month. From memory £120 for my Kirium 4 years ago.
In my experience it never comes back quite in the state it went there. Customer service is shocking. Last time I complained I was told I need to ‘stop complaining and trying to get freebies out of them’. I wouldn’t have complained if they had done the job properly. A letter to the MD of LVMH got no reply until I followed it up.
So take your watch to the local independent jeweller and get them to change the battery for a 5ver.
Would I buy another TAG? No chance.