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We investigate the scalar emission from binary neutron stars in shift-symmetric scalar-tensor theories with kinetic screening (<inline-formula><mml:math><mml:mi>K</mml:mi></mml:math></inline-formula>-essence), using <inline-formula><mml:math><mml:mrow><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></inline-formula> numerical simulations in the decoupling limit. To construct static binary initial data in the regime where the screening radius <inline-formula><mml:math><mml:msub><mml:mi>r</mml:mi><mml:mo>*</mml:mo></mml:msub></mml:math></inline-formula> greatly exceeds the orbital separation, we introduce a hyperbolization of the static field equations that bypasses the Keldysh-type breakdown affecting direct time evolutions. For equal-mass binaries, where the scalar emission is dominated by the <inline-formula><mml:math><mml:mo>ℓ</mml:mo><mml:mo>=</mml:mo><mml:mi>m</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math></inline-formula> mode, kinetic screening acts nonmonotonically on the scalar radiation, suppressing or enhancing the quadrupolar amplitude depending on the relative size of <inline-formula><mml:math><mml:msub><mml:mi>r</mml:mi><mml:mo>*</mml:mo></mml:msub></mml:math></inline-formula> and <inline-formula><mml:math><mml:msub><mml:mi>λ</mml:mi><mml:mn>22</mml:mn></mml:msub></mml:math></inline-formula> (with <inline-formula><mml:math><mml:msub><mml:mi>λ</mml:mi><mml:mn>22</mml:mn></mml:msub></mml:math></inline-formula> the wavelength): for <inline-formula><mml:math><mml:msub><mml:mi>λ</mml:mi><mml:mn>22</mml:mn></mml:msub><mml:mo>≪</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mo>*</mml:mo></mml:msub></mml:math></inline-formula> it is suppressed relative to the Fierz-Jordan-Brans-Dicke (FJBD) case, while for <inline-formula><mml:math><mml:msub><mml:mi>λ</mml:mi><mml:mn>22</mml:mn></mml:msub><mml:mo>≳</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mo>*</mml:mo></mml:msub></mml:math></inline-formula> it is amplified above FJBD. For unequal-mass binaries a scalar dipole reemerges, growing linearly with the mass asymmetry, while the quadrupolar screening remains close to the equal-mass case down to mass ratios <inline-formula><mml:math><mml:mo>∼</mml:mo><mml:mn>0.6</mml:mn></mml:math></inline-formula>. The nonmonotonic behavior of kinetic screening that we uncover has potential implications for gravitational-wave-based tests of gravity. The relativistic double pulsar, in particular, requires <inline-formula><mml:math><mml:msub><mml:mi>r</mml:mi><mml:mo>*</mml:mo></mml:msub><mml:mo>≫</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>9</mml:mn></mml:msup><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>km</mml:mi></mml:math></inline-formula> to efficiently suppress the scalar quadrupole; for cosmologically-motivated <inline-formula><mml:math><mml:mi>Λ</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math><mml:msub><mml:mi>r</mml:mi><mml:mo>*</mml:mo></mml:msub><mml:mo>∼</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>11</mml:mn></mml:msup><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>km</mml:mi></mml:math></inline-formula> (for a solar-mass source), giving only moderate suppression.