Re. use of 'thinners'... The effectiveness of this will all depend on the nature of paint/substance used to make the white dots, which may or may not have been originally applied to aid alignment. If the white is a 'convertible' coating (e.g. nitrocellulose, vinyl, thermoplastic acrylic...what people call "lacquers") it will dissolve in 'cellulose thinners' (i.e. one having a ketone content e.g. acetone/MEK/MIBK etc). But if it's a convertible coating (e.g. epoxy, amino-acrylic, alkyd etc...what people call "enamels") then it won't actually 'dissolve', but may start to shrivel after a few application.
But your main problematic question is... are the white blobs 'sandwiched' between layers of 'varnish'? If so it will mean that you will end up having to take off a small portion of the final coat of varnish (the bit over the top of, and around, the white blobs) ..a varnish which will almost definitely be an enamel...which is most likely to shrivel rather than dissolve.
If you're a tackle tart then its an exercise fraught with danger. You could gently sand the blobs off and then re-varnish those bits, but I'd use a marker pen or the like if it bothered me (which it wouldn't).
ATVB
N.B... you could always dip a blunted toothpick or the like in some nail varnish remover and apply it to one of the dots and see if has any effect. If it dulls/matts the surface but doesn't remove any of the white then you know its attacking the final coat of varnish. As long as you don't leave the nail varnish remover on long enough to shrivel the varnish you'll be able to remove the 'dullness'/restore the gloss with a bit of car polish or the like.
IMHO