Bored as I can't sleep so from a very non-scientific internet search I'd say it could be an issue. I calculated the mSv you'd accumulate flying from 65N to 65N via the North Pole (OULU, Finland to FAIRBANKS, Alaska -
North Pole-ish as I got bored trying to think of airports that were suitably located), you'd get a dose of 0.0615 mSv per flight (conservatively estimating 7hrs for each sector). If you did 900hrs a year doing this same flight, you'd pick up 8 mSv of cosmic radiation. EASA 'recommends' that air crew don't exceed 6 mSv a year, so that's potentially more, but not excessively more than the recommendation. I'm not sure how the radiation calculator calculates the figure, but maybe in some cases it's worth investigating further. Perhaps you could buy a commercial dosimeter? Although I'd imagine a pair of lead plated boxer shorts would be cheaper!
From the CAA website (link below)
Individual monitoring is to be regarded as best practice but it is recognised that this can impose unjustifiable cost for some operators. In these circumstances an acceptable course of action would be to rely on an assessment of maximum doses where this shows that air crew will not be approaching annual doses of 6 mSv. A suitable cut off point would be where the assessment indicates a maximum annual dose of 4 mSv. Where air crew are liable to receive doses in excess of 4 mSv per annum, it is recommended that there should be monitoring of individual air crew member's exposure using computer program prediction. The purpose of such monitoring would be to ensure that annual doses did not exceed 6 mSv.
Where an assessment of maximum doses indicates that air crew are liable to exceed 6 mSv per annum, individual monitoring must be carried out. In addition, operators should adjust an air crew member's roster to reduce exposure with the aim of preventing, where possible, doses in excess of 6 mSv per annum. Records for individuals exposed to more than 6 mSv per annum must be kept for a minimum of 30 years from the last annual exposure of more than 6 mSv (even if the individual concerned is deceased) or until the individual is 75 years of age, whichever is the longer period of time.
https://www.caa.co.uk/Our-work/About...mic-radiation/
Feel free to check my maths at the sites listed below the screenshots.
https://www.sievert-system.org/#Calcul
Great Circle Mapper