The paper and its accompanying supplementary material doesn't make clear if the multiplexed barcodes are found in the adapters or inline within reads, but a simple FastQC run would let you know if these barcodes are inline within reads: there would be a huge spike in the "per base sequence content" at the position corresponding to the inline barcode.

The tag is in the reference genome.

I am not 100% sure about the math, but if I am not mistaken, the chance of not seeing a particular 8-mer on a 2.2Mb genome is:

( 1 - 1 / ( 4^8 ) ) ^ ( 2.2 * 10^6 ) = 2.6 * 10^(-15)

Which is practically zero, so any given 8-mer will most likely be found on Neissieria genome (assuming 0.25 probability for each base).

Ans they should be unique to each isolate (which is not in this case either)

They should be unique to each isolate being sequenced on the same lane of a flowcell. Two different isolates can have the same barcode if they are sequenced on different lanes.

Should I remove them before alignment?

If there is a systematic enrichment on sequencing reads indicating the barcodes are inline within reads, then you could remove - this would be essential for genome assembly, for example. But most short read mappers (like BWA or Bowtie2) would soft-clip these bases, so for mapping you need not worry too much.