The construction with the adverb "πιο" (in your example "πιο γρήγορα", or alternatively "όσο γρηγορότερα", the comparative degree of the adverb γρήγορα) makes the assurance more strong; it is a standard expression in Greek and I don't think we can talk about a difference as long as the expression without "πιο" isn't normally used, except possibly in rare cases by some speakers.“Θα επιστρέψω όσο πιο γρήγορα μπορώ”
1) Θα συνεχίσουμε όσο καλά μπορούμε’
2)Θα συνεχίσουμε όσο πιο καλά μπορούμε’
Εντάξει , καταλαβαίνω τώρα .The meaning per se is the same in both sentences, but as I wrote above the construction normally used is the one with "πιο", which gives a more strong assurance with the comparative degree (καλά<>πιο καλά).