How to Add Customizer Setting in Child Theme

OK, check out the theme developer handbook.

$wp_customize->add_control( 'reblog_number_control', array(
  'label'    => __( 'Number of Reblogs', 'tesseract-child' ), 
    'section'  => 'tesseract_footer_options',
    'settings' => 'number_of_reblogs',
    'type'     => 'text',
    'priority' => 10
) );

Since you are in the child theme

'title'       => __( 'Reblog Options', 'tesseract' ),

shoudl be

'title'       => __( 'Reblog Options', 'tesseract-child' ),

In other words, your setting, control and section names need to match in add_control, add_section, add_setting.