A protestor holds a banner outside the Greek parliament during in a demonstration by municipal contract workers in Athens, Greece, on Thursday, June 29, 2017.

Analysts remain unconvinced that Greece is over its troubled economic past, despite a warmly received upgrade on Monday by the ratings agency Fitch.

The yield on the five-year Greek sovereign bond dipped by 5 basis points Monday following the upgrade, with Fitch citing improved economic conditions in the southern European country. The country's 10-year bond yield had also dropped more than 14 points basis last Friday, showing that investors are turning more confident on the embattled economy.

However, some market participants are still cautious about the medium to long-term prospects of Greece and are watching out for plans from the euro zone to make Greece's debt more sustainable in the long term.

"Greece is definitely turning a corner, as it will exit its economic program successfully unlike the two other programs. On top of that, after growing by 1.3 percent in 2017, the Greek economy is likely to outperform the euro area this year," Yvan Mamalet, senior euro economist at Societe Generale, told CNBC via email.

"However, the medium-term fundamental situation remains problematic," he said, "without significant debt relief measures, such as the ones recommended by the IMF (International Monetary Fund), the Greek debt level would most likely remain at (an) unsustainable level."

European creditors have agreed to grant some relief to Greece by making its debt more sustainable. However, the final details of such debt restructuring are still being prepared. Nonetheless, they are expected to be implemented only after the program has come to an end, which is scheduled to take place in August, and only if market conditions require such measures to be triggered.