Polypropylen is a so called a thermoplast. It can be melted and get solid again, so all the containers, cups,etc. like Tupperware are made. So there should be no problem. Other Plastic like phenoplast or aminoplastic are duroplast typs which goes decomposition when heated., this will change of course.
To the contrary, melting and remelting plastic causes cumulative degradation that is readily apparent after just a few cycles - mechanical, optical, and chemical properties all change, and usually not for the better. We (my colleagues and I) process polymers routinely, and we rigorously avoid remelting/reusing. We stick to one melt cycle, that's it. Polypropylene is particularly susceptible to oxidative degradation, especially at high temperature, so bear that in mind. Also, volatile and non-volatile additives in the polymer, which are important for maintaining polymer function, including long-term stability, are also affected by melt processing. Slip agents, anti-oxidants, etc., can all be lost during repeated melt cycles, which invariably lead to degraded performance of plastics.
More to the OP's point: "food grade" isn't well-defined in this context. But you can be sure that remelting plastics in the way you describe will result in polymers that do not have the same performance as pristine resins. Obviously, remelting is a big part of the recycling process, but recycled plastics are not merely melted and recast. Other chemical and physical treatment steps in industrial environments ensures that recycled plastics retain desirable properties, but even in this case recycled polymers may often not suitable for high performance applications.
Personally, I would not use remelted polymers for food applications (outside of industrial processes managed by people who know what they're doing).