Possible problem 1:

A pretty common issue with colony PCR is that some amount of successfully assembled, but untransformed, plasmid ends up on the recovery plates. When picking colonies for PCR a small amount of this plasmid ends up in the reaction mix and gets amplified, resulting in a false positive band. It doesn't take much.

It's more labor intensive but if I'm having this issue I pick a good amount of each colony, poke a little of it onto another agar plate then suspend the rest into 50 µL TE buffer. Then I centrifuge the tubes to pellet (which is usually barely visible), remove the supernatant, resuspend in 50 µL of TE then use 1 µL of that suspension for my PCR templates. That typically removes background template. Other times I've also just patched a bunch of colonies on a new plate and then performed colony PCR on the patches the next day.

I imagine that centrifuging your recovery, removing the spent supernatant, then re-suspending the E. coli pellet in an equal volume of fresh LB/SOC/whatever growth media then plating the washed cells would also accomplish removing most of the untransformed plasmid as well but that's not helpful unless you want to perform the transformation all over again.

Possible problem 2:

Colony PCR can sometimes amplify unintended sites in the chromosome of your cloning E. coli strain, and given the dirtiness of the reaction, sometimes even primers that behave well on purified DNA can produce odd products.

You said your primers didn't create a product on the extracted pDONR plasmid, but you might want to run a negative control with your primers where you pick a colony of your cloning strain into the tube. An even better negative control is to run a tube with a colony of your cloning strain that contains the empty vector. Then you can see if the band you're getting is just a background artifact.

Those places are where I would start trouble shooting before trying to figure out if it's something weird with your insert.

I agree with Alexandra Johnson answers, there are many causes of background false positives. Another way around it is to use different PCR for the colony PCR that are on the vector but flank the cloning site (and ideally would not be present on the source plasmid). This should circumvent the false positive problems.

Nope.

Colony PCR is notorious for false positives, especially if you are picking from the selection plate. If you insist on doing colony PCR, you need to streak out colonies of interest on a new plate & start a liquid culture from that streak plate.

I'd make a streak plate, set up a liquid culture and do a proper plasmid prep. As my advisor said, "You can't rush quality".