<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2007-03-19</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000350066</issuerCik>
        <issuerName>INTER TEL (DELAWARE), INC</issuerName>
        <issuerTradingSymbol>INTL</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000902111</rptOwnerCik>
            <rptOwnerName>MIHAYLO STEVEN G</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>P.O. BOX 19790</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>RENO</rptOwnerCity>
            <rptOwnerState>NV</rptOwnerState>
            <rptOwnerZipCode>89511</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Profit Sharing Agreement</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2007-03-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                    <footnoteId id="F2"/>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>5179498</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On March 19, 2007, a wholly owned affiliate of the reporting person reinstated a previously expired letter agreement (the &quot;Reinstated Agreement&quot;) with RBC Capital Markets Corporation (&quot;RBC&quot;), pursuant to which the reporting person agreed to pay RBC an agreed upon topping fee in the event that (a) a third party transaction in which a majority of the capital stock or assets of the issuer is transferred for consideration to a person not affiliated with the reporting person or the issuer (a &quot;Third Party Transaction&quot;) is consummated during the term of the Reinstated Agreement or during the twelve months following the term, and (b) such Third Party Transaction is subsequent to any offer (whether written or oral) made by the reporting person to the issuer relating to a transaction whereby a majority of the capital stock or assets of the issuer is transferred for consideration to the reporting person or otherwise becomes beneficially owned by the reporting person.</footnote>
        <footnote id="F2">One profit sharing agreement with respect to 5,179,498 shares of common stock of the issuer.  See Note 1 above.</footnote>
        <footnote id="F3">The topping fee, if any, is payable in cash to RBC within 5 business days of the closing of such Third Party Transaction.  On June 14, 2006, INTL Acquisition Corp. (&quot;IAC&quot;) an entity jointly formed by Vector Capital Corporation and an affiliate of the reporting person, made an offer to acquire for cash all of the outstanding shares of common stock of the issuer, other than shares beneficially owned by IAC.</footnote>
        <footnote id="F4">Twelve months following the termination of the Reinstated Agreement.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Steven G. Mihaylo</signatureName>
        <signatureDate>2007-06-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
