Missing tax card

I moved to Luxembourg as a resident on an EU Blue card in March, but after enquiring about some payroll issues with my employer today it came to light they don’t have a tax card for me (I understand this is meant to be automatic).

How can I get a Tax Card? Any idea how long this would take? The tax rate I am paying is higher than it should be (I should be tax class 2), is there any way to get the extra tax I have paid back this tax year (I.e without a tax return)?