Single phase utility power connected to 3 phase system
Using a three phase panel normally used with 208/120 three phase supply with 240/120 supply can be electrically sound and may even be code compliant.   But I am assuming the question is about a 240/120 split phase temporary power panel set on a pole, with a feeder running to an existing three phase panel that was installed with 208/120 three phase supply.  There could be a number of issues.

If there are three phase motors or other loads connected for 208Y, they obviously are not going to run right and may be damaged.

As mentioned in @Peter Green's answer, if there are multiwire branch circuits, you won't get the expected cancellation on neutral conductors, which could quickly result in overloaded on the neutrals.

If there are 208V circuits for appliances etc. (water heaters, baseboard heaters, etc.) they may see 0V or 240V depending which two legs they are on.  Those that see 0V won't run at all (but don't be fooled and think those wires aren't hot).  Those that see 240V - some could be unaffected and run fine; some could run differently than expected; and some could be damaged.