Answer : 2. "close the deal"
Explanation :

The most appropriate option to fill in the blank is:

close the deal

The sentence would then read: "The contingent managed to close the deal successfully."

Explanation:

"Park the deal" doesn't make sense in this context. "Park" usually refers to temporarily setting something aside or storing it.

"Heal the deal" is not a commonly used phrase. While "heal" can metaphorically refer to repairing or restoring something, it's not typically used in the context of deals.

"Catch the deal" doesn't fit the context either. "Catch" implies capturing something, but it's not idiomatic when referring to completing or finalizing a deal.

"Close the deal" is the correct idiomatic phrase used to indicate completing a negotiation or agreement. It fits well in the context of business deals or agreements being finalized.