The often quoted example of Lamarkism is the elongation of a giraffe's neck. Now, the giraffe did not 'learn' how to have a long neck. But this is Lamarkism.
How is the orange speckling of the froggies any different?
In Lamackism the giraffe might stretch its neck a little bit to get some food. Somehow (and there were some fun theories, including by Darwin) the acquired trait may 'feedback' into the chain of inheritance so the children of the giraffe have the slightly stretched neck.
In the frog example some frogs would have to somehow produce orange speckles by effort. I'm guessing if I asked you to do that, you might have some difficulty. How do you do the equivalent of stretching to 'reach' for orange speckles? The most 'likely' method is that eating the orange plants (or eating something that eats the orange plants) results in a transfer of pigmentation causing the frogs to become speckly. IF this characteristic could be inherited it would be Lamarckism.
But speckliness isn't all that we're worried about. There are other ways to cope with predation than blending in. They could change their development cycle (which is in fact what many animal populations 'try' first) so they have either more children (to counteract the number that will die from predation), or they have children at a younger age (to counteract their reduced life expectency) or something similar. If predation is really fierce, and they survive we might even see the frogs falling all the way back to living in perma-larvae stage!
So really, the question is, where did the orange speckling come from? Was it a mutation that lead to a frog being born speckly when it's parent's were not? Or was it a change that occurred to a parent after the parent was born that it then passed on.
The former is basic Darwinism, the latter is Lamarckism. The real picture is more messy than that. But that's the key difference: the origin of the speckliness.
If it was a genetic copying error around the reproductive event it was random mutation.
If it was an event during the normal lifetime of a frog that fortuitously lead to it developing orange speckles, then that is an acquired characteristic.
If it happened without foresight it was chance.
If it happened through some effort, inadvertent or otherwise, that might be 'felt need'.
Since frogs almost certainly have absolutely no clue what the best strategy is, they probably don't close their eyes and wish for speckles really hard in order to obtain them.
™ Version 4.2