The main reason Karamanlis was reluctant for Freddy's funeral to take place in Greece was not about a fear of an upsurge of monarchist sentiment, the real concern was that A-Pap would try and exploit it as an election issue. Indeed, in October that year PASOK won the election - 1981 was also the year of Greece's entry into the EEC and many feared that a PASOK victory would put a stop to it.* Initially K vetoed the idea for the above reasons, and in the context of the time it was based on a perfectly legit desire to avoid any potential disorder. It was when King Juan Carlos requested permission that K's hand was forced on the subject and only said yes to avoid an international incident - something he resented greatly.
To put this in perspective, Prince Peter had died a year earlier and was eventually buried in Denmark when permission could not be secured for burial at Tatoi, meaning that his body was left in the morgue for a month before a burial could be arranged.
*In the end they did not.