Your fixed monthly ‘Flex date’ is the 15th.

When switching to Dal Vrij on 06-05, you pay for the period up to 14-05, which is 9 days.

And 9/30 × 119,95 ≈ € 35,99

If needed, you can switch again from 06-06 and get unused days back.

Edit: what @Tochjo said 

If you look closely at the middle column labeled ‘Toelichting', then you can see you're not paying double, but for separate periods. It seems you changed your season ticket from NS Flex Basis to NS Flex Dal Vrij during your subscription month.

When you change your NS Flex season ticket, this doesn't change the date of the month that you receive the invoices. You first get an intermediate invoice for the remaining period of that subscription month, in your case of 9/30 × 119.95 ≈ 35.99 euros (for nine days), and then you get a monthly invoice every month on the same day that you used to before for a full month, in your case of 119.95 euros.

This means you weren't charged extra and there's nothing to claim back.

If you look closely at the middle column labeled ‘Toelichting', then you can see you're not paying double, but for separate periods. It seems you changed your season ticket from NS Flex Basis to NS Flex Dal Vrij during your subscription month.

When you change your NS Flex season ticket, this doesn't change the date of the month that you receive the invoices. You first get an intermediate invoice for the remaining period of that subscription month, in your case of 9/30 × 119.95 ≈ 35.99 euros (for nine days), and then you get a monthly invoice every month on the same day that you used to before for a full month, in your case of 119.95 euros.

This means you weren't charged extra and there's nothing to claim back.