Chikli closed out each letter emphasizing that "it is of the utmost importance for me to reach out to you personally about this problematic incident."
Yad Vashem says it won’t be involved in group visits to any site suspected of distorting events.
Some may be "saddened we resolved the political crisis with Poland that began during the Lapid era,” Cohen charged on Monday.
Polish Deputy Foreign Minister Pawel Jablonski spoke out as the Histadrut called a nationwide strike to protest the government's judicial reform process.
Ties between Jerusalem and Warsaw have been strained following the Polish passage in 2018 of legislation against speaking of Polish complicity in the death of Jews during World War II.
The resumption of trips is seen by Israel as a sign of thawing relations with Poland.
On Tuesday night, Foreign Minister Eli Cohen spoke with his Polish counterpart Zbigniew Rau, the first such talks between foreign ministers of both countries in two years.
Israel had not hosted a Polish delegation in four years before this week's visit.