To encrypt the connection to the SQL Server TARGET then place the following in the 'Additional ODBC connection properties' box on the advanced tab:
ENCRYPT=yes; TrustServerCertificate=yes;
If they want to encrypt the connection to the SQL Server SOURCE then add an internal parameter named additionalConnectionProperties and use the following value:
ENCRYPT=yes; TrustServerCertificate=yes;
It will not show up in the Replicate log but you can verify that it is working by running this statement on the target SQL Server while the task is running:
SELECT session_id, connect_time, net_transport, encrypt_option,
auth_scheme, client_net_address FROM sys.dm_exec_connections