Going from the full rules here - Rules Link
An "opposed influence card" I would deem as a card which someone has already declared they are using a guard against to defend or has a reaction like Jupiter's Cock played against it. At least that's the way I would rule this but its just my opinion Example
Player A (Batiatus) play's a Scheme on Player B (Seppius)
Player B uses a guard and unsuccessfully stops the scheme.
Player B cannot now use Seppius special ability to raise the required influence to make it so Player A can no longer play the card to avoid it.
The same if Seppius was a third party and tries to raise the influence when not directly involved.
Player A play's a scheme.
- At this point Seppius could use his ability to raise the influence required.
If Seppius did not trigger Meddling. Player B play's Jupiter's Cock on the scheme. Seppius could not now raise the influence needed for Player A scheme which would result in both the original scheme and Jupiter's Cock being returned to the players hand. I guess this is to stop ret-conning the Jupiter's Cock and other such cards.