This is because GTCE tools doesn't have tool classes, GTCE maintaner confirmed that this cannot be fixed on their side.
Tested with mod versions (all latest at the moment of writing this issue):
TFC: 1.7.9.167
DT: 0.9.21
DTTFC: 0.9.15
GTCE: 1.10.5.582
Other DT trees are fine, I guess this has to do with "No Tree Punching" 5ccc97d, I may suggest to have an option to check not only tool class but also tool oredict (craftingToolAxe)

That's pretty strange, even TFC tools that don't extend vanilla tool classes have the tool class set. That's a forge tool classification that isn't related to inheritance or anything. I'm surprised that it's not doable. Let's discuss in #tng-addons.

Same problem

I was meaning to fix this in my own fork of GTCE. There's no real good way of fixing this on DTTFC's end so DTTFC shouldn't really explicitly make a case for it but urge GTCE devs currently to override getToolClasses in MetaItem or what not, since getToolClasses is made to be ItemStack-sensitive because of this very reason.

Please try it :)

Rong isn't the gtce dev, so chances of a fix for this getting released are slim. It's up to GTCE to fix it.

Yeah I can PR to GTCE but not in any interest in doing so at the moment. Working on my own stuff.