or you can edit the code by.
AdminCP > Customization > Your Theme > Edit HTML & CSS > updateWarning
and comment out
{{if $newVersion = \IPS\Application::load('core')->availableUpgrade( TRUE ) and member.hasAcpRestriction( 'core', 'system', 'upgrade_manage' )}}
{{if $newVersion['security']}}
<div class="ipsMessage ipsMessage_error" id='elLicenseKey'>
{lang="dashboard_version_info" sprintf="$newVersion['version']"}
{lang="this_is_a_security_update"}
<ul class='ipsList_inline'>
<li>
<a href='{url="app=core&module=system&controller=upgrade&_new=1" base="admin"}' class='ipsButton ipsButton_verySmall ipsButton_veryLight'>{lang="upgrade_now"}</a>
</li>
</ul>
</div>
{{elseif !isset( \IPS\Request::i()->cookie['updateBannerDismiss'] )}}
<div class="ipsMessage ipsMessage_general" id='elLicenseKey' data-controller='core.global.core.updateBanner'>
{lang="dashboard_version_info" sprintf="$newVersion['version']"}
<ul class='ipsList_inline'>
<li>
<a href='{url="app=core&module=system&controller=upgrade&_new=1" base="admin"}' class='ipsButton ipsButton_verySmall ipsButton_veryLight'>{lang="upgrade_now"}</a>
</li>
</ul>
<a href='#' data-role='closeMessage' data-ipsTooltip title='{lang="license_dismiss"}'>×</a>
</div>
{{endif}}
{{endif}}
so it looks like
<!--{{if $newVersion = \IPS\Application::load('core')->availableUpgrade( TRUE ) and member.hasAcpRestriction( 'core', 'system', 'upgrade_manage' )}}
{{if $newVersion['security']}}
<div class="ipsMessage ipsMessage_error" id='elLicenseKey'>
{lang="dashboard_version_info" sprintf="$newVersion['version']"}
{lang="this_is_a_security_update"}
<ul class='ipsList_inline'>
<li>
<a href='{url="app=core&module=system&controller=upgrade&_new=1" base="admin"}' class='ipsButton ipsButton_verySmall ipsButton_veryLight'>{lang="upgrade_now"}</a>
</li>
</ul>
</div>
{{elseif !isset( \IPS\Request::i()->cookie['updateBannerDismiss'] )}}
<div class="ipsMessage ipsMessage_general" id='elLicenseKey' data-controller='core.global.core.updateBanner'>
{lang="dashboard_version_info" sprintf="$newVersion['version']"}
<ul class='ipsList_inline'>
<li>
<a href='{url="app=core&module=system&controller=upgrade&_new=1" base="admin"}' class='ipsButton ipsButton_verySmall ipsButton_veryLight'>{lang="upgrade_now"}</a>
</li>
</ul>
<a href='#' data-role='closeMessage' data-ipsTooltip title='{lang="license_dismiss"}'>×</a>
</div>
{{endif}}
{{endif}} -->
either way works, through css or edit the html.