We had our bathroom floor tiled about 8 years ago but recently, we've noticed water bubbling up through the grout when you stand on some of the tiles. I want to remove the grout and redo it. How do you remove old grout without damaging the tiles? The grout gap is only about 2 or 3 mm.

There is a general purpose tool called by various names but originally called a Fein Multitool. It is an oscillating tool 20K rpm and takes a special grout removal tool either made of Tungsten or Diamond. There are now dozens of manufacturers of such tools and the name of them and price varies hugely. I no longer use a Fein but prefer the Bosch or Dewalt. (I am a retired odd job man)

Example:

eBay item number:390873033986

Same tool pops up in lidl/aldi for about £20

I would consider an exakt saw.

Also you can get the Worx Sonicrafter from B&Q

If you're noticing water bubbling up when you stand on them there's likely to be a bigger job to do than simply replacing the grout (unless you're after a quick fix).
If water has penetrated the tiles it will be sitting underneath.
Proper job would be to lift the tiles, dry out the sub-surface, re-bed the tiles and then re-grout.
Otherwise you risk all kinds of rot and nasties.
Cheers, Pewe10

Ditto what Pewe says, the water under the tiles needs sorting.

+1

+1 too. Water under the floor tiles is more than a grout issue and needs serious investigation

Thanks everyone. That souns like a great tool. I was planning to try and dry the floor with a hot air gun between the tiles. Is that not going to be enough?

Once the moisture gets "locked in" you have to remove the tiles to dry it out and I hate to say this, depending on the substrate, more remedial work may be required.

Angle grinder