From an introductory physics perspective, the answer is True. Energy is energy, whether as heat, sound, kinetic energy, potential energy, mass, et cetera. The only reason that the concept of 'energy' exists is because it is a conserved quantity. If Energy is not conserved then what is meant by "energy"? What quantity does it refer to? This is unclear.
Technically speaking, energy is only conserved on average since quantum transitions happen between states with differing energies. Quantum decoherence of energy eigenstates results in a probabilistic choice of energy outcomes. Those outcomes conserve energy on average, but not individually.
Then there is the matter of curved space-time, in which even classically (not quantum) energy is not conserved. So if you're talking about the collision of massive celestial bodies, I imagine (not 100% sure) that there is no "energy" quantity which is conserved. (Recall: energy only has meaning as this special quantity which is conserved through time! It also has other properties)
The point is whether or not the student understands the problem in context. Neither the teacher nor student should get embroiled in technicalities if it is clear that the student does/does not understand the answer to the question. The teacher should not withold marks if it is clear the student understood, and neither should they award them if it is clear the student is winning on a technicality that they don't even understand. (As above, you can massage the answer to "true" or "false" depending on context).
However there are also issues of equity. Suppose the teacher marked the student as wrong, but the student did in fact understand the true answer. The teacher cannot determine for certain whether this student is genuine about their understanding. If they award them marks, maybe other students who are less honest will attempt the same. Furthermore, what about the test records showing that one student received marks for a given answer while another did not?
The solution to all of this is either to abandon standardised testing (fat chance) or for the teacher to be clear and explicit about the context of problems, and any assumptions made. The teacher should have made a disclaimer at the start of the test:, i.e. "All questions are asked in the context of classical Newtonian mechanics.". However, in the absence of such a disclaimer, I think it's fair for them to expect students to answer based on the level of physics taught in their course. I assume you are not being taught quantum physics or general relativity, in which case the reasonable answer to the question is True, energy is conserved in a Newtonian collision between bodies.
Note how I was clear about my answer being contingent upon Newtonian physics? I used to make such clarifications in my schooling because I frequently encountered the situation you've described here. I understood the answer but did not understand the question. I have concluded that such a situation is invariably the teacher's responsibility. They should award marks if you understood but the question was poorly phrased, despite the equity issues above. It is worse to rob a student of marks than to award extraneous ones. Robbing marks affects your grades and future prospects in a very real sense, if you have ambitions of higher education.
In my experience, teachers and professors were understanding of these issues and usually did award marks when I pursued the matter. However sometimes the teacher (and on rare occasions the professor) actually does not understand the answer themselves, in which case it's up to you whether you feel it's worthwhile to pursue a formal appeal process.