Water Hardness

No, water conditioners don't remove hardness. Things like running peat in the filter or using lots of bogwood will remove a bit of calcium but not much. I'm afraid there is only one, expensive way t lower hardness to any significant degree and that's by using RO (reverse osmosis) water. Either mix your very hard water with RO or use all RO with remineralisation salts added.

A quick summary:
pH is a measure of acidity; it actually measures the amount of hydrogen ions in an upside down way so the more hydrogen ions, the lower the number
GH or general hardness, is what is meant when we say this fish likes soft water and that one likes hard water. It is a measure of divalent metal ions, which to all practical purposes in tapwater means calcium with maybe a bit of magnesium
KH, carbonate hardness, is a measure of the amount of carbonate and bicarbonate in the water. Water companies call it alkalinity as it is measured by adding acid to a sample of water and measuring how much acid it takes to drop the pH to a certain value (4.5 if I remember correctly). High KH takes a lot of acid, low KH doesn't take very much.

They are inter-related to some degree. Carbonate stabilises pH. The more there is, the more difficult it is for the pH to change.
And they all tend to be high or low together, though you can have high pH with soft water. My pH is 7.5 and my water company classes my hardness as moderately soft.

I don't know what mm/l is measuring. 38mm of what. 127ppm calcium works out at about 7dDH. This is medium hardness, or moderate hardness, perhaps at a push it might be hard, it certainly isn't very hard. It should be fine for most tetras (I'm not sure which model you have)

Would de-ionised water work?

Yes it would, it's just as good as RO. Either mix it with your tapwater to get the hardness you want (you would need a GH tester) or add remineralisation salts to get the desired hardness. If you did use DI water, you would have to use it mixed or with added salts at every water change as using pure tapwater to do say an emergency water change would alter the chemistry of the tank enough to harm the fish. And of course when starting to use DI you'd have to start slowly and build up to gradually change the tank water.

Copied this from my water sippliers website

HARD WATER
The area supplied by Affinity Water has 'hard' water. The hardness occurs naturally and is characterised by the presence of high levels of calcium and magnesium, which are good for healthy teeth and bones.
CALCIUM   127 mg/l
Calcium is the principal constituent of hardness.
TOTAL HARDNESS   318 mg/l
Total hardness is usually expressed in terms of calcium carbonate and is measured in milligrammes per litre (mg/l) or parts per million (ppm). The recognised classification scheme we are using is: 0-75 soft, 76-150 moderately hard, 151-300 hard, 300+ very hard. Your water is very hard.
Degrees English (or Clarke)   22
This hardness measurement is used on some British appliances.
Degrees German   18
This is used on some German appliances.
Degrees French   32
This is used on some French appliances.
MILLIMOLS   3.2 mmol/l
Millimols per litre. Some appliances refer to water hardness in millimols per litre (mmol/l).
FLUORIDE   0.15 mg/l
Fluoride naturally occurs in the water in many areas. Affinity Water does not add any fluoride to your water. Fluoride is measured in milligrammes per litre (mg/l).

That is hard!

No Sue, that is "very hard"; Can't you read!

Actually, I would call that "Very very hard".