No se pueden pasar parámetros de entrada al procedimiento almacenado

Prueba este -

CREATE PROCEDURE [dbo].[tp_SelectTransactionHistorySearch] 
(
    @OffSetRowNo INT,
    @FetchRowNo INT,
    @StatusSelection NVARCHAR(MAX),
    @isReviewed BIT,
    @ProjectCaseNumber VARCHAR(MAX),
    @CostPageNumber VARCHAR(MAX),
    @TransactionTypeChange VARCHAR(MAX),
    @DescriptionChange VARCHAR(MAX),
    @TrasactionCreateOnBeginDate DATE,
    @TransactionCreatedOnEndDate DATE,
    @TransactionUpdatedOnBeginDate DATE,
    @TransactionUpdateOnEndDate DATE,
    @ItemID VARCHAR(MAX)
)
AS
    SELECT TH.TransactionID
        ,  TH.IsReviewed
        ,  TH.ItemID
        ,  TH.CostPageNumber
        ,  TH.Comments
        ,  TH.CreatedBy
        ,  TH.CreatedDateTime
        ,  TH.UpdatedBy
        ,  TH.UpdatedDateTime
        ,  TH.TransactionDescription
        ,  TH.TransactionTypeID
        ,  IAccrualByItem.PROJCASE
        ,  IAccrualByItem.USTSTAT AS TransactionStatusID
        ,  TStatType.Name AS TransactionStatusTypeName
        ,  TStatType.[description] AS TransactionStatusTypeDescription
        ,  TType.Name AS TransactionTypeName
        ,  TType.[description] AS TransactionTypeDescription
        ,  COUNT(*) OVER () AS TotalCount
    FROM TransactionHistory AS TH
    JOIN TRVMVSDDVW001.INTERFACE_Files.dbo.DBATUSTA AS IAccrualByItem ON TH.TransactionID = CAST(IAccrualByItem.USTTRNNBR AS INT)
    LEFT JOIN dbo.TransctionStatusType AS TStatType ON TStatType.TransactionStatusTypeID= IAccrualByItem.USTSTAT
    LEFT JOIN dbo.TransactionType AS TType ON TType.TransactionTypeID = CAST(TH.TransactionTypeID AS INT)
    WHERE TStatType.Name = @StatusSelection
        AND TH.IsReviewed = @isReviewed
        AND IAccrualByItem.PROJCASE = @ProjectCaseNumber
        AND TH.CostPageNumber = @CostPageNumber
        AND TH.TransactionDescription = @TransactionTypeChange
        AND TType.[description] = @DescriptionChange
        AND TH.CreatedDateTime BETWEEN @TrasactionCreateOnBeginDate AND @TransactionCreatedOnEndDate
        AND TH.UpdatedDateTime BETWEEN @TransactionUpdatedOnBeginDate AND @TransactionUpdateOnEndDate
        AND TH.StatusID = 1
    GROUP BY
          TH.TransactionID
        , TH.IsReviewed
        , TH.ItemID
        , TH.CostPageNumber
        , TH.Comments
        , TH.CreatedBy
        , TH.CreatedDateTime
        , TH.UpdatedBy
        , TH.UpdatedDateTime
        , TH.TransactionDescription
        , TH.TransactionTypeID
        , IAccrualByItem.PROJCASE
        , TransactionStatusID
        , TStatType.Name
        , TStatType.[description]
        , TType.Name
        , TType.[description]
    ORDER BY 
          TH.TransactionID
        , TH.ItemID
        , TH.CostPageNumber
    OFFSET (@OffSetRowNo - 1) * @FetchRowNo ROWS FETCH NEXT @FetchRowNo ROWS ONLY

Actualización n.º 1:

Configure esta opción, antes de ejecutar su consulta -

SET DATEFORMAT dmy

o, más preferiblemente, usa ISO formato yyyymmdd -

EXEC @return_value = [dbo].[tp_SelectTransactionHistorySearch]
    ...
    @TrasactionCreateOnBeginDate = '20130310',
    @TransactionCreatedOnEndDate = '20132003',
    @TransactionUpdatedOnBeginDate = '20130520',
    @TransactionUpdateOnEndDate = '20130604',
    @ItemID = NULL

Actualización n.º 2:

DECLARE @temp TABLE
(
    string VARCHAR(10)
)

SET DATEFORMAT dmy 

INSERT INTO @temp (string)
VALUES 
    ('10-03-2013'),
    ('20-03-2013'),
    ('20-05-2013'),
    ('04-06-2013')

SELECT CAST(string AS DATE) 
FROM @temp