I have used 5 gallon pickle buckets as well and had your concern. I don't think it had any impact on syrup flavor.
A ways back I got to some thinking about this kind of thing.
Smell detection does not really mean you will be able to taste anything from the smells source. However, we by nature think that we will, mostly because it often does.
Taste buds are designed to work off much larger/substantial/sizable amounts of substance. Your nose is designed to work off MUCH smaller particles.
You do not taste with your nose, you taste with your tung a much different organ.
When I was suspicious of my green pickle buckets that still smelled of pickles, and after washing them well they still smelled, I went after the source with my tung and buds, so I stuck my head up inside the bucket and licked the side of the bucket to see if I could taste pickles.
I could not, so I trusted in my taste buds over my nose and used a few.
Now .... only a small percentage of my collection was done with pickles pails so my test scenario is NOT solid.
Additionally, if you are going to stow/stew for any considerable time sap/syrup in polymers with a preexisting smell, all money and bets are off the table for me.
Also, if your pickle pails are green like mine are, they will warm your sap measurably faster than white buckets will.