An INSERT statement triggers the SQL Server Audit to write it down in the logs although INSERT is not listed as an Audit Action
The optimal approach would be to disable the INSERT audit for that table, but since you seem to have a peculiar situation, here's one way of dealing with it:
Once you made sure the INSERT audit is not enabled by connecting to the audited database and running this query:
-- List enabled database specifications
SELECT  a.audit_id,
        a.name as audit_name,
        s.name as database_specification_name,
        d.audit_action_name,
        s.is_state_enabled,
        d.is_group,
        s.create_date,
        s.modify_date,
        d.audited_result
FROM sys.server_audits AS a
JOIN sys.database_audit_specifications AS s
ON a.audit_guid = s.audit_guid
JOIN sys.database_audit_specification_details AS d
ON s.database_specification_id = d.database_specification_id
WHERE s.is_state_enabled = 1

You can filter that audit to avoid the inserts from being registered. The Create a Server Audit and Server Audit Specification doc says:


Optionally, on the Filter page, enter a predicate, or WHERE clause,
to the server audit to specify additional options not available from
the General page. Enclose the predicate in parentheses; for example:
(object_name = 'EmployeesTable').


The Filter page can be found by right click the audit &gt; properties. If you prefer, the T-SQL to alter the audit not to register the inserts would be something like this:
USE [master]
GO

ALTER SERVER AUDIT [Your_Audit_Name]
WHERE (NOT [statement] LIKE 'INSERT%')
GO


Some relevant content:
Filter SQL Server Audit on action_id / class_type predicate
sys.fn_get_audit_file (Transact-SQL)
How to analyze and read SQL Server Audit information