Insert set value into DB
A possible solution would be to create a #tmpHold table with the same columns as #tmp minus the dbSet column.  Insert the results of the exec into #tmpHold and then insert into #tmp the data from #tmpHold plus the extra column @dbSetc.

create table #tmpA
(
    idx int identity(1,1),
    lpath nvarchar(260)
)

------------ ADD ALL DB Backup Files below ------------
insert into #tmpA (lpath)
    Select 
    'C:\temp\db.bak' union select
    'C:\temp\db1'
------------ END EDIT ------------

create table #tmp
(
    LogicalName nvarchar(128)
    ,PhysicalName nvarchar(260)
    ,Type char(1)
    ,FileGroupName nvarchar(128)
    ,Size numeric(20,0)
    ,MaxSize numeric(20,0)
    ,FileId tinyint
    ,CreateLSN numeric(25,0)
    ,DropLSN numeric(25, 0)
    ,UniqueID uniqueidentifier
    ,ReadOnlyLSN numeric(25,0)
    ,ReadWriteLSN numeric(25,0)
    ,BackupSizeInBytes bigint
    ,SourceBlockSize int
    ,FileGroupId int
    ,LogGroupGUID uniqueidentifier
    ,DifferentialBaseLSN numeric(25,0)
    ,DifferentialBaseGUID uniqueidentifier
    ,IsReadOnly bit
    ,IsPresent bit
    ,TDEThumbprint varbinary(32)
    ,SnapshotUrl nvarchar(128)
    ,dbSetC int
)

create table #tmpHold
(
    LogicalName nvarchar(128)
    ,PhysicalName nvarchar(260)
    ,Type char(1)
    ,FileGroupName nvarchar(128)
    ,Size numeric(20,0)
    ,MaxSize numeric(20,0)
    ,FileId tinyint
    ,CreateLSN numeric(25,0)
    ,DropLSN numeric(25, 0)
    ,UniqueID uniqueidentifier
    ,ReadOnlyLSN numeric(25,0)
    ,ReadWriteLSN numeric(25,0)
    ,BackupSizeInBytes bigint
    ,SourceBlockSize int
    ,FileGroupId int
    ,LogGroupGUID uniqueidentifier
    ,DifferentialBaseLSN numeric(25,0)
    ,DifferentialBaseGUID uniqueidentifier
    ,IsReadOnly bit
    ,IsPresent bit
    ,TDEThumbprint varbinary(32)
    ,SnapshotUrl nvarchar(128)
--  ,dbSetC int
)
declare @countr as INT
declare @size as INT
declare @dbSet as INT
declare @tmpPath as nvarchar(260)

SET @countr=1
SET @size=(SELECT count(*) FROM #tmpA)

WHILE @countr &lt;= @size
BEGIN
    SET @tmpPath = (SELECT lpath FROM #tmpA WHERE idx = @countr)
    SET @dbSet = (SELECT idx FROM #tmpA WHERE idx = @countr)

    TRUNCATE TABLE #tmpHold;
    INSERT INTO #tmpHold    --insert results of EXEC into #tmpHold
        EXEC ('RESTORE FILELISTONLY FROM DISK = ''' + @tmpPath + '''') --need to add @dbSet to dbSetC column
    INSERT INTO #tmp    --insert #tempHold + @dbSet into #tmp
        SELECT *,@dbSet FROM #tmpHold
    SET @countr = (@countr + 1)
END